By RICHARD COHEN Washington Post Service They won't let me see her. They say she has been through so much and her privacy needs to be protected. I understand. They say she is sick and that she lives in a Detroit nursing home under an assumed name.

All they want for her is the insurance money her late husband paid for before he died. His name was Eddie Slovik and he was executed Jan. 31, 1945, as the order read, by musketry. The charge was desertion. So I can't tell you what she looks like now.

I can tell you what they told me. Arthritis has crippled her. She is 63 years old. She was born-with a congenital hip problem and old age hasn't helped it any. She has epilepsy, too. She spends much of her time in a wheelchair and she lives, when room and board are deducted, on about $25 a month from her Social Security check. Her name is Antoinette Slovik, and her husband was the only American soldier since the Civil War to be executed for desertion.

THERE IS a book about the case. It is called "The Execution of Private Slovik," and a movie for television was made about it. The Army never changed Eddie Slovik. He was always a misfit, always a waif never combat material. They gave him a gun anyway and told him to fight. Read his letters. He was in the Army 372 days and he wrote Antoinette 376 letters. He wrote that he cried all the time. He called her "Mommy" in the letters, although they have no children, and he told her how he hated the Army, how much he missed her, and how he

remembered those weekend afternoons when he was finished working as a plumber and they did nothing but make love. He was not the ex-con his record says he was nothing mean or tough about him. In the Army, he cried a lot.

THERE WAS nothing complicated about Eddie Slovik. He was a nice man, but a weak man. It was 1944 when he went into the Army and he was just one of those left at the bottom of the manpower barrel.

It's clear in retrospect that Eddie Slovik should not have been a soldier. To some, it was clear even then. This is what his commanding officer in basic training, Arnold C. Shaw, wrote just last year: "I was Eddie Slovik's commanding officer during his 17 weeks of basic training. I didn't know his tragic fate until 1954. We recognized this man's total inability as a combat soldier … We tried every means to get his discharge.

Failing this, we tried to get his transfer to a noncombat unit . . ." The letter is in a file in Medina, Pa., at the law offices of Bernard Edelsen. He is also the lawyer for Robert DeFinis, a public relations man. In 1974, DeFinis got into a conversation in a supermarket with a man named Edward P. Woods. They talked about the Slovik case and Woods invited DeFinis to his house to view the television movie about Eddie Slovik. Woods is a man who doesn't forget. In 1945, he was Capt. Robert Woods, and he was Eddie Slovik's defense counsel.

BETWEEN THEM, the two say they have probably spent something like $25,000 on the Slovik case. They have written letters to presidents, asking for a pardon, but they have been told that dead men can receive no pardons. There is no one to deliver the pardon to. They have written to congressmen and senators, asking for laws and resolutions. Recently, they engaged Edelson and he has filed something called an "Application for Correction of Military Records." All the men want is Eddie Slovik's insurance for his widow. Slovik paid $6.70 a month for a $10,000 policy that is now worth about $68,000. His widow could use the money. There are complications. The policy Eddie Slovik bought had a clause in it. The clause said "No insurance shall be payable for death inflicted as lawful punishment for crime." But there are other papers and they indicate that the generals from Eisenhower on down never intended to strip Eddie of his benefits, only of his life.

They had no intention of punishing Antoinette. IT MAKES no sense anymore to assess blame for what has happened. It was a different time and a different place. Men did what they thought they had to do. One of them was Dwight David Eisenhower, who had a desertion problem on his hands and who approved the execution. Another was a nobody from Detroit named Eddie Slovik, who thought he could find a way out of the war by declaring himself a deserter. He knew about the Army and he knew about jail and he thought the Army was worse. Lots of men made that decision in World War II. Forty-eight of them were sentenced to death. Only Eddie Slovik died. So sometime before the end of the summer the Army will take another crack at Eddie Slovik. There are 3,248 cases under review, and his is one of these. The man at the Pentagon said it usually takes 180 days to dispose of a case, but he doesnt know about this one. "It's an unusual case," he said, "unlike any we have had before." WILLIAM C ALLEY has been for-given for My Lai, and Tokyo Rose has been forgiven, and the Vietnam War resisters have been forgiven. Will the United States government somehow find a way to help the widow of Eddie Slovik? She's old and sick now.