In the UK, people in hospital who possibly shouldn't be there, for whatever reason, are sometimes described as "taking up a bed" (i.e. tying up a valuable resource of the health service unnecessarily). Apart from that, I agree with @MaxWilliams. I like the image though.

If someone is just sitting around doing nothing you can say that they're keeping the chair warm. It isn't usually used for beds as far as I know.

Is the original idiom intended to sound humorous?

@hmijail, yes, it is.

@MariaDeleva Just curious, what language or nation is the original idiom from?

@AJFaraday, Bulgarian

@MariaDeleva Cool! I really like the idiom, by the way. Just wanted to get that right if I use it in conversation.

Possible duplicate of What do you call a sick person who is lying in bed?

@ArmenԾիրունյան, I don't think it is a duplicate as the other question does not cover the humorous aspect of this one.

@MariaDeleva: My bad, I did not realize you were looking for a humorous equivalent (do note that the highest_voted answers on both questions are the same).

Interesting idiom. It is similar to saying that someone who is idlely leaning against a wall is holding it up.

I would be keeping the bed company :-)

Maybe "keeping the bed warm."

That phrase is fantastic. I think the best answer might be that we introduce it into English.

Funny, there is a closely related German phrase ("das Bett hüten" ≈ "guarding the bed") and it's so idiomatic that I completely failed to see the humour in it, until now.

Similar idea to "holding the wall up" (used when someone is leaning against a wall, obviously not doing any work).

"Holding the bed down" would have roughly the same meaning and any reasonably clever person would get it with enough context. Not idiomatic, however.

In French you would say something that translates as "being nailed to the bed"

The Texas Aggie Bonfire crew has the idiom of a “helium log” that requires a person to sit on it to keep it from floating away.

Can you clarify whether you're asking for a phrase that relates to the "suffering of the illness", or the "being in the bed" part? Perhaps in your country a teenager/student also might "keep the bed from running away" - not because they're sick but because they lie in bed until 4pm. From an English perspective, I can more easily suggest phrases for being very unwell ("calling for Huey", "shouting soup") than I can for being in [stuck] in bed

For now I really like "keeping the bed company", but it is just a comment and not an answer and I can't accept it. Also I like holding down the fort and perhaps it sounds closest to the original.

"Holding down the fort" sounds like a confusion between "holding the fort" and "batten down the hatches" to my ears. Cambridge dictionary says the "down" is optional, and it sure seems to make it make less sense. In terms of sickness, I wouldn't really say it's applicable to this situation as it generally refers to the process of ensuring things keep on going as they should in the absence of some usual authority or control process (like when your boss goes on holiday).

"Keeping the bed warm" or "keeping the bed company" is probably the closest. Other words could be used in place of warm/company if they're a relevant physical or emotional effect a human being would have on an object. To work as a joke, the effect should be one that the bed wouldn't need in order to perform its function/be a bed. While looking into idioms for sickness I came across a very amusing list at linkydinky.com/blowchunks.shtml

In our family, we sometimes joke that the dog, who loves her comfort and seldom leaves the bed, is "making sure the bed doesn't fly away". More of a family joke, though, than a widespread idiom.