How to handle tenants attempting to break lease?

[Joshua D.]

We have, currently, 18 units. All are rented and tend to, typically, do pretty well. We do year-long leases with each tenant and currently don't offer an early termination clause in the lease. However, we have a tenant who has lived in one of our units for 16 years. We bought the property in May and had her sign a 1 year lease, and she got ahold of us yesterday and requested a written approval for HUD for a 30 day notice. We initially explained that we couldn't approve the request, because her lease wasn't up until May. She then wrote back a paragraph of "issues" that we were never made aware of, such as mold, flooding, sewage backup (basically a bunch of BS) and said it wasn't safe for her to live there or her kids, blah blah blah. You guys know the deal.

Anyway, we initially dug our heels in and stood our ground, stating that we wouldn't break the lease and that if she did, HUD could potentially terminate her Section 8 voucher. (She is the only tenant that we have who is on Section 8.) She then wrote us an email basically begging to be let out, stating that she already found other housing and put down the security deposit, etc.

At this point, I don't want to keep digging in our heels and possibly have her threaten us with legal action or "withhold rent for repairs," etc. It just feels like it could turn into a headache.

In these types of situations (HUD or no HUD, all of our tenants are on the same lease terms with us,) what do you typically do when tenants want to break their lease?