If they insist on staying, then they abide by the contract, period.Tenants threaten to sue all the time.

sounds like someone got a nasty gram.. we see this with the syndicators that are called out then threaten the investor who called them out.. or anyone else companing about a service only to have the company either threaten or tell them if you take this down or retract we will give you your money back.. kind of like landlords lying about how great their dead beat tenant is to just get them to move on to the next landlord. 

Threatening each others' safety is never allowed.

After a few nasty emails and him threatening to sue me if I left a bad review, I paid him in full, $7000 and moved on.

Months later, Tenant then accuses me of “threatening” her because of the keys situation.

One tenant screamed at my husband threatened lawyers the whole 9.

Instead, he wrote a threatening letter (first contact since closing) and demanded thousands of dollars. 

On June 7th, we sent an itemized list of deductions via text; he responded on June 8th, disagreeing and threatening legal action.

Owner ended up settling with the tenant, but then we had to threaten to sue our own client to get them to pay our legal fees.- Owner must sign a Hold Harmless to indemnify us against any potential tenant lawsuits relating to the work their contractor is doing.--- Another lawsuit resulted from owner's contractor taking down basement handrail to get supplies down the steps, then they didn't put it back and tenant fell down the stairs.- We also negotiate a reasonable completion date, depending on the Scope Of Work (SOW). --- Who gets all the phone calls and wastes time calming a tenant down because the owner's contractor doesn't show up as scheduled after they took time off from work or a 3 day job takes 3 weeks?

I also always keep my rent increases in line with the local market, so sometimes I'll have tenants threaten to leave sometimes, and once they do their research they realize that it wouldn't make sense at all to find another property and end up paying the same thing.