If the building you are living in becomes infested with mice, it is the obligation of your landlord’s insurance to pay for damage and other costs related to the infestation. However, there are some pests not covered by insurance on either end. Bedbugs, for example, which may be connected to a single unit are not usually covered by tenant insurance or landlord insurance. You will need to pay out of pocket, unless you find an extended policy option that includes them.