can i convert my Imac that has no Mac OS work as a monitor for a mini mac

Have you attempted to re-install Mac OS on it from the Recovery Partition (Command + R on startup)? If you have and the computer will not start up there likely isn't anything wrong with the OS, it's suffering from a hardware failure which is likely the HD.

However to answer your original question, the computer must be fully functional to work in TDM which is fully explained in Use your iMac as a display with Target Display Mode - Apple Support

This is highly unusual, as a computer won't just decide to lock you out all of a sudden. There is always a way. I'd be looking into those ways, instead of trying to figure out how to declare it a brick and just use it as an expensive display.

Since you seem to have a Mini, I would get a USB stick,

download the latest macOS from the App Store on the Mini

(don't install), and make a USB installer.

Then, power up the iMac holding down the Option key.

Select the USB stick to boot up from. Once booted,

you can do a First Aid on the internal drive and reformat

and install macOS from USB.

It is a iMac (Retina 4K, 21.5-inch, Late 2015).

That iMac model is too new to support Target Display Mode per the article that rkaufmann87 linked:

iMac (Retina 5K, 27-inch, Late 2014) and later iMac models can't be used as Target Display Mode displays.

The last iMac to support TDM were the Mid-2014 models.

Which model of iMac is it?

Please explain what you mean when you say critical Mac OS failure. What are the indications of this failure?