If the long-term tenants are moving there could have been some unique arrangement between them and the old owner that they know is unlikely to continue.I know a lot of investors avoid inherited tenants whenever possible but I think it can work in the right situation.  

I inherited a tenant in a househack that was on ODSP.

The current 'landlord' inherited the house so he is not landlord savvy and the tenants took full advantage.  

Agreed, since you inherited the tenants I assume you have no ties to them, so you don't have a reason to give such a huge discount every month.  

When I inherited some tenants, I had my agent give them notice that I needed them to vacate in order to do updates.  

Yes, I was hoping for owner financing because the wife inherited the property because the husband died and was a horrible landlord.  

I am inheriting a lease on a rental property.

One of the units is occupied with a new lease so we are inheriting those tenants.

I/we recently inherited a 1/2 acre lot with a small cabin on it, It had all originally belonged to my Mom, but then she suddenly passed away a few years ago and left it to me and my Brother.

We inherited 2 tenants in the property and were very fortunate that they were good people.