Seller withholding sec deposits as "fines" and not transferring?

[Ross Miller]

I'm a fairly new investor in the process of buying a 5 unit. This is my first multi-unit property, and it is also the first time I'm inheriting tenants. We are expecting to close in mid to late October. I am working with an agent that I've used before for SFRs, but I don't think she's done many multi-units. The seller is not really an experienced landlord. She never intended to own this property but actually bought it to bail out a struggling family member. 

As part of the seller's lease, if the tenants violate the lease, she keeps their security deposit. Two of her tenants do not yet know that they are losing their security deposits. She says that at closing, she will write me a check for the security deposits that will be in full, and I can ask the others to pay a security deposit at the start of my lease. Apparently my agent also advised that this was acceptable. 

Am I off base thinking that this is wrong? And I feel like my agent may have overstepped by claiming that this is okay. My thoughts are that if the tenants violated her lease, they should be paying her their fines, and the security deposits should remain in tact. I feel like I should receive the full security deposits at the time of closing. What if the tenants get mad when they find out they're losing their deposits and decide the trash the place and move out 2 hours after closing. Now I have no deposits to cover any damage. Even if they don't do that, now I have to chase tenants around to get security deposits. What if they don't have that much cash siting around - now I'm sending pay or quit notices already?

Just wanted to check with the more experienced folks before I call my agent.