"Keep the bed from running away"; equivalent idiom in English?

It's not super common, but I have heard holding down the bed to mean "staying in bed for a long time". I don't think it necessarily implies illness, though; you could be holding down the bed just because you're lazy. Some example usages (bolding added):

And for anyone who thinks Lyme Disease is no big deal, I invite you to revisit a post I wrote last fall about the ugly, ugly realities of late stage Lyme - because I wouldn't wish this hell on anyone. Now hike up those socks and go have some fun for me. I'll be here at home, holding down the bed. (Source)

Had sickies around all last week, and am now sick myself. I have never been so sick! Gonna take me awhile to finish recovering, including housework! I at least looked over this last post, will be trying to think of creative ways to do these as I am holding down the bed! (Source)

To end this long and rambling story, I was sick and did not make the annual family Thanksgiving gathering. I did get a delivery of leftovers (Thanks Mom) but no family drama on the side. I spent the rest of the holiday holding down the bed or my miniature sofa. (Source)

However, it definitely isn't just used for illness. For some reason, this phrase as a synonym for "lying in bed" is especially popular for pets:

It's not quite a set phrase; there are some examples of the version holding the bed down (which I just noticed @JimmyJames mentioned in a comment), but holding down the bed appears to be the more common choice for figurative use (for example, an image search of "holding the bed down" has pictures of truck beds much more prominently displayed than sleepy pets).

The idiomatic expression "bedridden" comes close to what you are referring to:

• Confined to bed because of illness or infirmity

  • bouts of fever sometimes kept him bedridden for months at a time.
  • she was bedridden and unable to move her hands.

(AHD)

The expression is quite old:

• also bed-ridden, mid-14c., from adjectival use of late Old English bæddrædæn "bedridden (man)," from bedrid, from Old English bedreda, literally "bedrider, bedridden (man)," from bed + rida "rider" (see ride (v.)).

• Originally a noun, it became an adjective in Middle English and acquired an -en on the analogy of past participle adjectives from strong verbs such as ride.

English is for the most part lacking in highly specific idioms however one of it's strengths is that general idioms in different context can be quickly adapted and understood by native speakers.

User Josh61 ultimately gives the most specific idiom with the same meaning as yours with bedridden. However, this doesn't have any of the humorous overtones you were looking for.

Therefor, I would propose the following adaptations of 2 general idioms, (I've actually used both) that convey the same meaning when used by a sick person.

The first is Good friends.

These last couple days my bed and I have become good friends.

This suggests you've spent lots of time in bed but you're taking it in stride and can laugh at it.

The second would be Overly acquainted.

I've become overly acquainted with my bed this last week.

This suggests the same thing, lots of time in bed, but in a more annoyed and sarcastic way.

I would try something like "guarding the bed", "keeping the bed under watch"... surely not idiomatic, but understandable and conveying the humorous original meaning/intention.

(It's interesting that some say they wouldn't understand it, makes me wonder about the mother tongue. I'm Spanish, and though I don't think we have any similar saying, I do think we have similar enough word playing that it would be well understood, either the translation of these versions or of the original one - even if it was a one-off thing invented in the spur of the moment)