Lot's of questions.
1. How much of that water bill balance is actually from a burst pipe?
2. If they were delinquent prior to, say, ~November, during "non-extreme" weather months, why wasn't the service disconnected?
3. If #2, there's some negligence on the water department's part.
Unfortunately, I believe the property owner is liable for municipal services in Texas. But just because you're liable, doesn't mean you'll end up liable for $20,000.00. Fight that $ amount for sure.
First step, get each unpaid bill and then get the most recent paid bill by the tenant and check the meter readings. Make sure only the month(s) that had a burst pipe have outrageous metered charges. I would request the number of months late that the city's last 5 disconnected accounts were. Compare that to your case and note any discrepancies.
I would finish the eviction for this tenant for sure, and even if they'll never pay, see if you can get an un-paid money judgement on them in your county. Both will show up on background checks.
Good luck!