Constable has failed to execute a writ.

Section 2.16 of the Penal Code read "he shall be liable to a fine for contempt not less than ten nor more than two hundred dollars, at the discretion of the court. The payment of such fine shall be enforced in the same manner as fines for contempt in civil cases."

We have not had to deal with this in the past.
Does anyone have any input into how to handle this process?

A constable can also be held in contempt under Local Government Code 86.024.

What sort of writ was involved?

If it's a writ of execution, also take a look at Civil Practice & Remedies Code 34.065. The law changed last legislative session, so depending on when the writ was issued, you may be able to use the former law.

Email me at tsellars@dallascounty.org or post more here and I'll see if I can be of further help.