For 23 years I've been doing rodent work in the DFW area. From houses to the major sports venues, I've learned some things. Some were taught to me. Other things I have learned on my own. Here are some helpful hints.
Never put out poison in a structure where people frequent, work, or live. If you do, two things are likely to happen. The next animal that finds it will likely die as the previous answer has said. Or, the bait will get old and grain beetles will hatch from it, and they will be your next pest problem.
Some people will try to convince you that some bait will make the rodent thirsty and they will leave to get water. Or, use this bait and they will die and not stink. Don't you believe it!
Locate entry points and do not seal last one until all rodents are eliminated from structure. If you do not find all the entry points, the problem will reoccur. If you seal them in, they will risk death to get out. But more likely they will chew through a wall or the ceiling and then the fun begins.
Mice will nibble on several different foods. Peanut butter as bait works but mice love cocoa products better so Snickers is my proffered bait of choice. Mice are stupid and will go back to trap even if trap has missed before. My record trapping time for a mouse using an old fashion snap trap is 40 seconds after I shut the office door. If bait on a snap trap is gone and the trap is still set, insects such as ants or roaches ate it. If you caught a mouse and the bait is gone, there is another mouse. Remember, the early bird gets the worm, but the second mouse gets the cheese!
Rats are somewhat intelligent. If you do not set a trap correctly and it missed, the rat is likely to never to go near it again. If deprived of water they will chew through a water line. Rats drink about an ounce of water every day. Leaving uneaten dog or cat food outside or inside is setting up a buffet for rodents. Extremely good climbers with exceptional balance and run the small power lines from poles to structures. Rats have poor eye site but can navigate in total darkness. They also have an excellent sense of smell. A dead rat in an attic or wall will smell for up to three weeks unless removed. The sooner you look for it, the better the chance of locating it. The odor tends to sink so if dead one is in a wall smell will be strong at baseboard. If it died in the attic under the insulation, you may not smell it until you remove the insulation right above it.
If you can find a dead rodent and remove it, you can try a product called X-O Odor Neutralizer. Apply directly on spot. Your local hardware store may have it.