Is there any mattress which can absorb urine passed in the night?

Those bed pads are great, they do not leak through and are washable. Or a vinyl mattress cover that goes under the sheets. Those work great and just wipe it down with diluted bleach in a squirt bottle

Have you tried bed pads that are placed on top of the sheet? They are for incontinence and some are reusable. I'd guess they would be easier than changing mattresses (though you may need a new one if there have been accidents) . Search for 'bed pads for incontinence'.

My mother had a similar problem. We did not know at the time, that she had congestive heart failure. Ask an experienced nursing home director, how they handle these problems. My Mother uses Depends, but there is no more constant wetting.

the "tranquility" overnight briefs are AMAZING!! also Amazon has reusable bed pads which help ALOT with the bed issue ... if you can't afford that, then get vinyl shower curtains and lay them over the mattress and under the sheet. this will protect the mattress if you can't get a zip on mattress protector. they do sell mattress pads which are "waterproof".

You are dealing with a very difficult situation. I am going to ask you a few questions about your MIL which may make it easier to help you.
Why can't she move, sit up etc.
What is wrong with her apart from the diabetes .
Is her blood sugar well controlled
Can you get or afford if available absorbent undergarments or make washable pads from many layers of cotton fabric like sheets or towels
What was the reason the urine tube (catheter) did not work
Did it give her pain in her bladder.
How long has she been unable to move
Has she recently had a stroke
Are you able to keep her skin in good condition
Is her skin red, have rashes or ulcers(bed sores)
Having her lie on a urine soaked mattress would not be a good idea because urine soaked skin becomes sore and infected very fast.
The only thing that comes to mind is something called a Cholera mattress. I have only seen pictures not used them. But they appear to be plastic or rubber covered with a hole in the center and a bucket placed on the floor to catch the feces from a patient with Cholera.
If you did something like that I would want a thick sheet over the rubber because of the heat . You would cut a hole larger than the hole in the mattress so it does not get wet but put a removable fabric layer round the hole. her skin should be kept very clean and protected with a thick layer of whatever is available to you for babies bottoms. Plain Vaseline is better than nothing .I realize in your part of the World medical supplies are difficult to obtain and very expensive. But if protective undergarments can be obtained and changed every two hours that is the ideal solution. Changing her position if tolerated is also essential. If you can not do that make fabric rings to rest her elbows and heels.
There may be other people in your part of the world who know more about recourses available or those who have lived there.
job one is to get the diabetes under control and that will lessen the number of times she has to pass urine. Please come back others will have plenty of ideas.