I said that he left most of his money with Marina. Not all. And, of course, Oswald followed the Russian tradition or wearing his wedding ring on his right hand. Assuming that you are even correct that most of his co-workers didn't know he was married, that is probably because he hardly spoke to anyone and wore his ring on the opposite hand. Not because he didn't wear his wedding ring on a regular basis. Instead his own wife confirmed it was the only time he had done so. She was in the best position to know.
From "Marina and Lee". On the morning of the assassination after dressing "Lee kissed the children, who were sleeping. But he did not kiss Marina, as he always did before he left in the morning. He got as far as the bedroom door, then came back, and said "I've left some money on the bureau. Take it and buy everything you and Junie and Rachel need. Bye-bye." Then Lee went out the door.
"Good God", thought Marina, "What has happened to my husband that he has all of a sudden got so kind?"
When she awakened later and "Looked into the bureau, she found the extraordinary sum of $170. It must have been nearly everything Lee had."
He didn't leave the money in his wallet as he normally kept it. He took it out, placed it on the bureau and specifically told her to spend it all on her and the girls. All of it. No worries about tomorrow and tomorrow and tomorrow......