Person 2 should not be scared of using the law. You haven't said where you are, but the basic principles, especially at the small claims level, are fairly universal.
Before anyone can sue you they need to write a formal letter telling you what you owe and why you owe it. At that point you can just hand over the money and be done. Or you can write back and explain why you disagree. (The one thing you DON'T do is ignore it). So if Person 2 moves out they don't need to worry about suddenly getting a lawsuit out of the blue; just wait and see if they get a letter.
Conversely, using a small claims court is generally pretty easy. Go to your relevant government website (find it using e.g. "atlanta small claims" or "georgia small claims" if you live in Atlanta) and follow the instructions. No lawyers needed (usually). Like most things, the first time you do it its all a bit scary, but the system is there for people like you and Person 2 to get what you are owed. If you won't use it because you are too scared, well then people will walk over you and get away with it. The courts are where you get to fight back.
Edit: NYC information
A bit of Googling found this web site with lots of relevant information. Fact sheet 9 covers apartment security deposits.
The security deposit must be kept by the owner in an interest-bearing account in a New York State bank. The owner must notify the tenant of the name and address of the bank and pay the tenant the full annual interest, less 1% of the security deposit per year for the owner's administrative costs. The tenant can choose whether the interest is to be subtracted from the rent, held in trust until the end of the tenancy, or paid in a lump sum at the end of each year.
A security deposit should not be used as a final month's rent. At the end of the lease, if the tenant honored the terms and conditions of the lease and left the apartment in the same condition as it was when initially rented, except for normal wear, the owner must return the full security deposit. If damage was done, the owner may apply part or all of the security deposit to the cost of repair.If the tenant disagrees with the owner over the return of the security deposit or payment of interest, the tenant may begin a proceeding in small claims court or contact the Consumer Frauds and Protection Bureau of the New York State Attorney General.
These information sheets are meant as a guide to the law rather than being the law itself. Assuming that the law for a room is the same as for an apartment, it sounds like the answer to your question is "No". However it also sounds like Person 1 has failed to put the deposit in a separate interest-bearing account, which would definitely count against them if they tried to sue.
The problem is that Person 1 might claim that there is damage to the room rented by Person 2, so that has to be taken from the deposit and hence money is still owed for the rent. There needs to be an agreement about any damage to the room, and that means giving notice.