Inherited tenants, no proof of security deposit

[Bertha T.]

So my husband inherited a multifamily home in illinois when his dad died. We moved in to the first floor. And now have also inherited tenants in the upstairs apartment. These tenants didn't have a signed lease. They are leaving in 2 months and are asking for their security deposit. 

However, we don't know if the departed father ever collected a security deposit from the tenant. We asked for a receipt or any kind of proof. The tenant has none. Now they are bringing up lawyers.

I am at a lost. Are we liable for a security deposit when there is no proof of one or how much?