I agree with Lynn. Everything needs to be documented and put into writing. If this goes to court, that letter will be exhibit A. Make sure that it's detailed, easy to follow - with bullet points highlighting important events - and unemotional. Just stick to the facts.
The fact that the landlord waiting until just a few days ago says a lot about the facts here. If your sister had just broken the lease on December 1, the landlord would have - should have - acted much much sooner. The fact that he's only acting now, more than a month later, confirms your sister's story. (Imagine a judge asking the landlord why he waited a month to go after the tenant if the tenant had in fact broken the lease. The judge just won't buy whatever answer the landlord manages to stumble through.)
And yes, your sister did have a lease, but the landlord agreed to end the lease because he had signed a new tenant. The fact that this new tenant didn't work out is not your sister's responsibility. He should have had her keep paying until he got the first month's rent and security deposit in hand. The fact that this guy is inexperienced or just dumb is not her fault. Same thing with the busted pipes.
At this point, I would respond with that detailed letter and politely tell the landlord to pound sand. The next move is his.
John