I have a simple home theater mini stereo system in my bedroom
that I use for television and VHS viewing.
It recently stopped outputting a signal to the speakers.
However, headphones still work with it and the speakers work on my
other system. Nothing works through the speaker outsputs.

Can someone give me an explanation for this? I'm trying to figure out
whether it can be fixed or not.

I'm not sure but may be there's something wrong with your amplifier section. that's why it's not outputing to your speakers but works on headphones.

Could be a fuse is blown.

thanks,

I'll look into those possibilities.