If you plan to replace your floor covering and throw out the old rug you may decide to leave it down as long as it doesn't make it impossible to paint the floor trim. In most cases you will want to use drop cloths and tape them down over the floor covering using removable masking tape.
Termites and other pest can cause expensive damage. Here’s what to look for: sawdust-like accumulations of frass indicate the presence of termites. An exterminator can spray or set traps to eliminate the infestation. A clean hole without cobwebs or leaves indicates an access hole for rodents. An exterminator can set a trap for them, too.