Sort the permission before the chewing
The first consideration is paperwork, not furniture. Check your tenancy agreement for a pets clause before the degus arrive, and if the wording is silent or ambiguous, ask the landlord or letting agent in writing and keep the reply. A small caged animal is an easy yes for many landlords precisely because the animal lives in an enclosure, and having that yes in writing removes the one dispute that could cost you the flat rather than the deposit. Photograph the room where the cage will stand, skirting boards and door frames included, on move-in day, so pre-existing scuffs are never laid at your degus' door later.
Noise deserves a line in the same calculation. Degus are daytime animals and mostly quiet, but a metal exercise wheel at dawn carries through a thin flat wall, so stand the cage away from the neighbour's bedroom wall and choose a solid-surface wheel that runs smoothly rather than a barred one that rattles.
A cage they cannot eat their way out of
Standard small-pet cages with plastic bases are short-lived housing for degus, who treat a plastic tray edge as a starting point and can open a hole in it over a few determined weeks. In a rental, an escaped degu loose overnight can do more damage than a year of supervised roaming, so the enclosure itself is your main line of defence. Choose an all-metal cage with a metal tray, narrow bar spacing, and doors that latch positively; degus learn sliding catches. Site it with clear air on every side — a degu can reach several centimetres beyond the bars, and wallpaper, curtains, cables and the leg of a bookshelf parked against the cage will all be trimmed to bar length.
Inside, give the chewing a legal workload: solid wooden shelves and ledges they are allowed to consume slowly, replaceable gnaw blocks, and a deep tray or digging box of substrate. A degu busy demolishing her own shelf is a degu with less appetite for the room.
Free-roam time in one defended room
Roaming is where rental damage actually happens, so confine it to a single room you have hardened in advance. Skirting boards are the classic casualty: a line of clear acrylic protector strips, or furniture and storage boxes parked along the most tempting runs, keeps teeth off the paintwork. Cables go into hard trunking or up off the floor entirely — a degu can sever a lamp cable in seconds, which is as much a safety emergency as a deposit problem. Door frames get the same protection as skirting at chewing height, and the door itself stays shut with a draught excluder filling the gap beneath, because a degu's whole body can flatten through a space that looks far too small.
Supervise every roam, and keep sessions in that one room rather than letting the degus graduate to the whole flat. One defended room is a system you can check; five rooms are five chances to miss a chewed cable behind a sofa.
A standing supply of legal things to destroy
Finally, budget for chew material the way you budget for food. Apple and pear wood sticks, willow sticks and balls, pumice stones, seagrass mats and good hay in constant supply all wear the ever-growing teeth down on items that cost pennies. Rotate what is on offer so the supply stays interesting, and scatter some of it around the roaming room before each session so the first chewing of the evening lands on your wood, not the landlord's architrave. Keep the room rules and chew supply written down where anyone letting them out can check them, because that consistency is what returns your deposit in full. Family Sharing on KinsLe gives relatives you pick access to that profile.