Possible Clues:

• Always there to finish the mice off
• Disfigure mice at the end of a disease that's ever-present
• I'm in church up to the finish, being locally resident
• Characteristic to a particular field
• Restricted to a certain area
• Native to a spot
• Native to a certain region
• Harassed medic needs space to cope with it
• I may leave medicine that's dispensed for native
• Native half-starter in a little enclosure?