Zarinsky was charged last week with Durrua's murder.
Conway's attorney, Alton D. Kenney - Monmouth County's former first assistant prosecutor - said he will ask the court to immediately freeze an attorney escrow account in Zarinsky's name containing about $126,000.
"The amount of money here, we recognize, is finite, but if one of the results of this is that Mr. Zarinsky doesn't have the money ... to defend himself, that is an unintended result," Kenney told the Asbury Park Press for Friday's newspapers.
Zarinsky has been in prison since 1975 for killing another teenage girl. He said in court last week that he is gravely ill and that doctors told him he has about six months left to live.
For several decades, Zarinsky was largely forgotten. A bizarre set of circumstances led to charges in 1999 for the murder of Rahway Police Officer Charles Bernoskie, who shot to death in 1958 during a botched burglary at a car dealership.
Zarinsky was charged after being implicated by his sister, who only came forward after authorities linked her and her husband to the theft of $112,500 from Zarinsky's mutual fund, which he started with proceeds from the inheritance of their mother's house.
He was acquitted of Bernoskie murder, but was found responsible for it in a 2003 civil trial.
Zarinsky was ordered to pay $150,000 to the officer's widow, but last year an appeals court vacated the jury award, saying too much time had passed for Zarinsky to mount an adequate defense. The officer's widow was ordered to return the money to him.
The widow had given the money to her six children, and said she faced the loss of her home, but law enforcement groups raised money and she returned the $154,783. Zarinsky recently filed a notice that the amount did not include enough interest.
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Information from: The Star-Ledger, http://www.nj.com/starledger
