i had a muffler blowout and lost the parts

I'm assuming you lost the bottom end of your stock muffler. If so, make a new end for your muffler using the end of a beer/soda can with the drinking hole in it. Attach it with a hose clamp.

Did the lost part look like this....

If so, pm me your addy and I'll send it to ya.

Short answer: No it won't hurt the engine.
It WILL be annoying, so I'd suggest doing what wheelbender said or something similar.
Or even better, PM xseler!

happens all the time to folks that don't double-nut the cap

i've had a few baffles fall off and never to be found, so I made my own baffle with some sheet metal, if you cut about a 4 inch circle out and draw a circle in the center the same size as the pipe and cut slits from the outside to the inside circle and make tabs, you can fold the tabs up and clamp it onto the pipe, I went a step further and fashioned a small tube that came out of the hole. I actually got more power out of the homemade baffle than the stock one due to the hole being bigger.
I added some high temp foil tape around the outside to seal it a little before I clamped it on.

I take 'em out on purpose, exhaust flow is better and LOUD PIPES SAVES LIVES!!!COP'S HATE IT...