Engine stalls are not viewed in the tail pipe. I had a JT-9 stall on me on the fence once about dusk, the precussion knocked the wind out of me and a fireball was visible accompanied by some quite warm air.
Old low bypass engines could and puke and choke regularly, hang around any airport with old dc-8/9's 707/27's and you are sure to hear a compressor stall, usually a couple at a time before recovery..
Newer engines, high By-Pass with variable stator blades to maximize the aoa of the compressor stators as the engine speed increases do not stall as often but are much more susceptable to damage as a result as like anything with more moving parts.
Most of the above posts did not mention the relation between the compressor blade and stator. It is not merely an airfoil it is one that compresses air trapped between the blade and the stator continously achieving a higher level of compression. If for some reason (advancment of thrust in most cases) the pressure of a fwd stage is unable to be guided to further compress we get a violent backflow of air out the inlet. That is the simpilest explanation as I understand and have experienced.