Quoted from mg81:

Land lording is a business, don't take it personally. Generally the best option with a problem tenant is to get them out as quickly as possible in a way that will not encourage them to damage the place or get you arrested. That way is often giving cash to the problem tenant. I know that you are already "in the hole" and you don't want to lose anymore money, but look at the numbers and see what makes the most sense.
I don't know your area, so I will use some numbers from my area.
Figure a non-paying tenant that is not damaging a property will cost you $500-1,200 per month in lost rent for a small residential rental. Figure it might take you 1-3 months to get them fully out of the property if you go through the legal system plus all of the legal fees to do that. So you are now out anywhere from $750 - $5,000. Add in any damage they do to the place plus the fact that they will leave it incredibly dirty and you will be out at least one week of rental to get the place rent-able and perhaps much longer. It might not even be in a show-able condition to try and get a new tenant for many weeks. Add up all of those costs, wasted time, headaches, etc.
What I would recommend is telling your tenants that "you appreciate their tenancy for all of these years, but the current situation will not work out, how much money will it take to get them to clean and fully move out of the place in the next 48 hours?".
They may tell you to go to hell, but if you are nice about it and at least pretend to be sympathetic to their situation they may give you a number that is far lower than the costs if you go through the legal system to get them out. Once you have gone through a bad eviction process with tenants trashing a place, giving them $500 - $1K (or more) in cash to quickly and voluntarily leave without damaging the place will seem very cheap.
Best of luck