Would think you would see some kind of evidence from either termites or rats ....
Rats:
would need escape entrances and exits - and need access to water & food...look for soil excavation in the form of dirt mounds with a hole beside it ......
control - there are wafer like products, that tear off into sticks ....(remove any pets before doing this)... you toss a stick where a rat might find it ...rat eats it - gets super thirsty ...then leaves area looking for water, then dies
Termites:
Cant live without moisture ....so they build "exterior tunnels" that go around not edible to edible food sources ... so do a walk-around of your property ...these tunnels look like saw-dust or dirt or a combo of both and about 1/4" wide or so .... these tunnels always lead back to a source of moisture, like mulch or constantly wet earth .....
Termites "swarm" at least once a year ..... where tens thousands emerge .... and fly off looking for something else to feed on .......
control - cant really help with a natural remedy .... except try to remove any mulch - and fix a possible leaky faucet ....
Would call termite control and get a free inspection and see what they say ....might also get a 2nd or 3rd opinion
have heard some plants can deter termites ...but have no idea how effective it is for an "entire" house
Best case .... the depressions or sinking is just from natural subsidence ....this happens has roots rot, or ground compacts itself under its own weight ...can also happen after heavy rains
