New bed
Just to be safe, I ordered a spare cover because I had sewn the fleece blanket from the original cover firmly onto it (see references, it’s supposed to be attached with Velcro, but that doesn’t even last a minute). Washing just the blanket makes no sense, it comes off straight away and then everything gets cleaned properly.
This spare cover is made from much sturdier material! I basically have a brand new dog bed now! Highly recommended! With this cover, I’ve also sewn the fleece blanket onto the bed cover again.