Hi Peter........I can see this small creature is an insect larva. What would make the most sense here, since it looks like it's running on furniture fabric---is a 'webbing clothesmoth.' See the attached pictures.

The tiny (5-7mm or so) tan moths are harmless---but they are the ones that lay eggs on potential feeding sites for their larvae. The moths may be seen on walls, furniture or fabric, but small size, weak flight and usually you are distracted by something else may not make them that noticeable.

Upon hatching, the tiny larvae 'graze' on fibers of animal origin---wool or wool blends. If you have an afghan made of wool or a blanket or other decorative item of wool on the furniture---that could be where larvae are 'grazing' on those fibers. They might also be grazing on the upholstery---perhaps along the seams or around the cushions or places that are otherwise difficult to reach or clean. You may notice a 'thinning' of the fabric or perhaps tiny holes in the fibers if the item is knitted or woven.

If you don't have wool items or woolen blends on this furniture, adults may be finding situations where their larvae can survive. The stuffing in upholstered furniture might provide harborage. So can soiled upholstery.

Probably the best you can do here is cleaning these and other items like it---carpets included. Vacuuming can be helpful; use the attachments that allow you to reach even the deepest folds in upholstered chairs. Pay special attention to seams, also---a good place for larvae to escape detection.

If you need to 'spot clean' the fabric where something spilled, that may be helpful, too.

Carpets can be vacuumed frequently and 'steam cleaned' regularly. Another place where these little creatures can cause damage---felt. Do you have any bookends (or decorative items) with felt glued to their bottom surfaces? You might take a look at those for evidence of damage.

For small items like bookends or decorative knickknacks, put them into small plastic bags and put them into the freezer for a couple of weeks. For blankets, afghans or a variety of clothing and winter-wear---dry-cleaning will kill the pests, but obviously, not fix any holes in them. Sometimes those items can be repaired and other times, discarded or used for something totally different.

I hope this is helpful.......

Webbing clothesmoth larvae produce fine filaments of silk. Using that and bits of natural fibers, they may cover and hide themselves, making them very difficult to see. Upon reaching maturity, they become very quiet and molt into an immobile, non-feeding stage called a pupa. After some period of time, they molt into the adult moth stage and the cycle starts over again.