Mass held up in corner by two tension forces?

I’m working on creating a pool of physics questions for my students, and I came up with one whose solution made me stop and think. I’m not asking for checking/proofing of my work, I think it’s correct. I just want some help/confirmation of my analysis of the results.

The problem has a mass hanging in the corner between a wall and ceiling. It’s held up by two tension forces (as shown in the illustration below). The strings are parallel, making the hypotenuse of a triangle with the wall and ceiling as the legs. The mass is static.

My solution necessitates the mass to be 0kg, so I interpret this as thinking that it’s impossible to hold up a positive mass with two strings in the way presented. The two strings would HAVE TO have at least a slight difference in angle for things to work out. I.e. there’d be a bit of sag in the system to accommodate gravity.

If my thinking is correct, that’s great… but then I think about extending this to a problem where the mass is held up by two rigid beams, not strings. So there, how would one reconcile the need for sag if it’s a rigid structure? Is there still technically sag but on a microscopic level?

I’m going to be teaching this soon, so I just want to make sure I’m brushed up on my reasoning. Thank you for any suggestions!