Late in his life, he moved to different hotels twice, due to unpaid bills. He spent his last ten years living in the New Yorker hotel (a quite new hotel when he first moved there in 1933 - it had only been built in 1930).

He was supported financially by the Yugoslavian government (including during WWII when they were a government-in-exile). When he died, his Yugoslavian pension was US$500 or $600 per month (I've seen both quantities given in sources). Westinghouse was also supporting him with $125 per month + paying his hotel bill. This was a large sum of money! Even if his Yugoslavian pension was "only" $500 per month, his annual cash income was worth about US$116,000 in current US dollars, and estimating by the New Yorkers' cheapest room rates, his rent might have been worth another $40,000 per year in current dollars.

On the other hand, he seems to have spent this money quite freely. He put plenty of money into his research, which he still continued, and also spent freely outside research (except on hotel bills)! Whether or not he had money, he doesn't appear to have liked paying hotel bills. The Governor Clinton Hotel wanted him to pay his $400 bill (about $6,000 in current dollars), he gave them a "death ray" in box, with instructions to not open the box. Since this death ray was supposedly worth $10,000, they accepted it. After Tesla's death, the box was opened, and found to contain a resistance box, a common electrical measurement device. He doesn't appear to have had any significant savings at the end of his life, and by that standard, he could be called "penniless", despite his substantial income.