Cash for keys is probably a controversial approach, but I've used it successfully.
If it looks like eviction is in the future, you might consider a "cash for keys" offer in which you say something like, "Look, I know this is tough news, but we're headed towards eviction. I can offer you a better option. If you can be completely out by (date and time), we'll give you (some amount of money), and we'll go through our normal move out process and maybe add some or all of the security deposit too, depending on the condition of the place. But if you aren't out in time, we can't honor this offer and we're going to have to proceed with the eviction. Do you want to talk about this option?"
Of course, the date would be sooner than what you would get with an eviction and it ought to be smoother, and less damaging to your property, because the tenant is choosing to leave instead of being forced to leave by you and the court.
Benefits are less stress and probably less unpaid tenancy or vacancy, and the tenant can get out without an eviction and with head held a bit higher. Plus extra money to help get into next place.
You'll be giving up money, but by speeding up the end of a bad situation it might be worth it. You'd have to judge that.
No doubt a search on "cash for keys" would bring up more on this approach.
We did this successfully with a tenant recently. We already had a (relatively) high trust relationship though.
