Laser is light stimulated by emission of radiation. You excite the source, it emits a photon, the photon is absorbed by another molec/atom of the source and reemitted. This keeps happening, the beams gets all collimated, monochromatic and awesome, then it bounces out of the source. The source material is a very specific shape to allow this.
Light decays as it travels. If you could somehow circumvent that, and the mirrors reflected all of it, then sure why not. But good luck trying to make light that doesn't get weaker as time goes on and a surface that absorbs no light at all or otherwise does not change the photon energy.
The idea of not being able to observe such an event is interesting too. It does seem to be the case the measurement changes the outcome of the system. Unless the hypothetical two way perfect mirror was constructed, which makes no sense, but that's why theory is fun.