ORANGE COUNTY, Fla. -- The State Attorney's office sent an offer to Anthony's attorney Jose Baez, to discuss the possibility of limited immunity. If the defense were to agree, the deal would likely keep her words from being used against her, but would not protect her from any other information that investigators dug up and potentially could find in a criminal case. Casey hasn't said a word to investigators about little Caylee Anthony's disappearance in 21 days.

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CAYLEE'S FATHER: FHP Report Could Help In Search For Caylee's Father
TEAM COVERAGE: Limited Immunity Offered To Casey Anthony
VIGIL: Anthony Family Raising Money For Search
EVIDENCE REMOVED: See Images | Watch Raw Video
ARCHIVE: Read Previous Reports Related To Anthony Case
MESSAGE BOARD: Talk About Anthony Case, Search For Caylee

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Channel 9's Kathi Belich was first to report the discussion of immunity. When Channel 9 asked Casey's mom Cynthia Anthony if the State Attorney's Office had made an offer to get her daughter to talk about Caylee.

"I don't know anything about that. We're not privy to that kind of stuff," said Cynthia Anthony.

Attorney Jose Baez had a different response.

"We talked about it, but there was no formal letter. Anything further, I'm not going to comment on," said Baez.

Jose Baez contends any information Casey has about her missing daughter has been filtered through him, to her family and then to law enforcement. He said investigators have not come to him with any specific information to ask Casey about.

GRANDPARENTS MEET WITH INVESTIGATORS AGAIN

Also on Monday, Anthony's parents, George and Cindy Anthony, met with sheriff's investigators. Monday's meeting was a continuation Friday's meeting that was cut short by a fundraiser for Caylee. The Anthonys met with investigators for nearly three hours and left the sheriff's office around 12:30pm. The Anthony’s praised sheriff’s investigators for their work in the case.

"They're working as hard as they can to find Caylee and that's their goal. We have to find Caylee," Cindy Anthony said.

Cindy Anthony has a scheduled visit with Casey at 1pm Tuesday.

A sheriff's office spokesman would also not elaborate on the specifics of the meeting but said detectives would follow up on any information they may have gotten. The sheriff's office did confirm that the FBI lab was helping analyze evidence in the case.

"No effort will be spared to exhaust any investigative method or technique," said spokesman Angelo Nieves. "It's extremely important we find Caylee."

Baez, the attorney for the mother of the missing toddler said he was going to appeal Casey Anthony's $500,000 bond to the Florida Supreme Court, but no appeal has been filed. Baez's office says attorney Michael Walsh is researching it. Casey Anthony has been held in the Orange County jail on charges of child endangerment and obstructing the investigation. She reported her child missing nearly three weeks ago and told investigators she had left the girl with a babysitter. Detectives suspect that babysitter doesn't exist.

Meanwhile, the State Attorney's Office has a little more than a week-and-a-half to decide if it's going to file any charges against Casey. Her father hinted Sunday she won't get away scot-free.

"She has to pay for some of the stuff that she put herself through and put her daughter through," George Anthony said.

Investigators expect to have results this week on crucial DNA evidence taken from Casey Anthony's car. Investigators said they found stain in the trunk of Casey Anthony's car, hair samples and a bad smell coming from the trunk. Police question if the stain is biological or not. That question is expected to be answered when the DNA test results from the stain come back this week. Sheriff's officials said they did not plan to release those results, however.

Eyewitness News asked Caylee's grandfather George Anthony what he expected the results to be.

"They are going to be what they are going to be. I have no control over it. I don't know what they are. I don't believe they are going to find anything," George Anthony said.

Eyewitness News has also learned that if the case becomes a homicide, which prosecutors have said is very possible, they could still go ahead with the case even if Caylee is never found, dead or alive.

"It would be proving motive, means, opportunity, the person who was last seen with or having the last knowledge of the person who has disappeared," said Bill Sheaffer, a well-known defense attorney.

In a case involving a child, Sheaffer said prosecutors would have a stronger case if evidence of a death could rule out other possibilities.

"Such as the child was abducted or the child wandered off," said Sheaffer

ATTORNEY DENIES RUMORED LETTER EXISTS

George Anthony visited his daughter in the Orange County jail Sunday to try to get more answers about his granddaughter's disappearance. When he emerged from the emotional visit, he said he had learned nothing new. He did say that Casey had given her attorney a letter that possibly contained clues about Caylee's disappearance.

However, when Channel 9 talked to Casey Anthony's attorney, he said all of the talk about the letter is absurd. He said the letter doesn't exist and he never asked for one in the first place.

It is still unclear if Casey is writing letters to her family. Casey's father seemed frustrated and said he asked Casey tough questions. He also admitted his daughter has made mistakes. Still, George insists his granddaughter is alive. He's so confident she will return, he's planning a birthday party for Caylee in a few days.

George Anthony said publicly that he will not let himself think about the worst-case scenario. He stated that he cannot allow himself to become negative. George said that his last encounter with his daughter Casey was an emotionally charged 45-minute conversation.

Investigators also said that Casey's ex-fiancée changed the story he told about hearing Caylee's voice over the phone days after her mother says she disappeared. Jesse Grund made another statement to deputies. Sources close to the investigation said the ex-fiancée stated that he is not positive he heard little Caylee Anthony on a phone conversation he had with Casey on June 24.

Grund released a statement to Channel 9: "I could not testify 100% that I did hear her on that specific phone call. I still believe that I did hear her, but I can't separate this call with other calls I have had with Casey in the past. I definitely stand by what I said that I heard Casey scold Caylee to get off the table during that call on June 24th."