BiggerPockets

Yes, you are responsible for the lease, including the security deposit. When you buy a property with a lease in place, the lease stays in place. Whatever security deposit they put into the lease when they signed is now your obligation to deal with (refund, use to repair damage, etc.) when they leave.

Normally, when you purchase a property with a tenant, you would get a credit from the seller for both the security deposit and for the partial month's rent. For example, you close on the 20th and the seller has already been paid rent for the month. You should get a credit for 10 days of rent.

Since you signed that addendum saying the deposit and prorated rents were not being transferred, you agreed to give up those credits.

Since it was a short sale, the seller may not have had the money. I wouldn't say they duped you, but they owed you this money and you agreed not to get it. Probably too late to do anything about it.

Sounds like the previous owner spent the security deposit a long time ago, i.e., he couldn't give you what he probably no longer had.

Sorry, but hopefully you got a good enough price that replacing the security deposit isn't too big a stretch.