That old dog was dormant for so long he was confused for a furry doormat, but a doormat is likely to stay dormant, or inactive, because it is lifeless: that old dog has some life in him yet.
Volcanoes are described as dormant when they stay cool for a long time, without spewing hot lava and ash. They may have the ability to come to life, but they remain dormant, or inactive. Dormant comes from French dormir, "to sleep," and it refers to living things that are on a break rather than things that have died. Being dormant is being temporarily at rest, although sometimes, as with some cancer cells, things become permanently — and thankfully — dormant.