The washine machine finished it's cycle but there was smoke coming out of the drum and a burning rubber smell

Sounds like the main bearing has broken.
Time for a new one.

Holly, always easier to buy an assembly, but probably a lot more expensive. If you can remove bearing and take to a industrial supplier and get matching bearing, the cost would be a fraction of that of a new drum assy. If you or a friend can do it, go for it.
You may want to get a second opinion on what you are smelling, it very well could be the drum rubbing gasket if it is a burning rubber smell.Maybe call a good appliance Tech. have them diagnose and estimate repair. Check LG washer bearing link below.
"I hope this helped you out, if so let me know by pressing the helpful button. Check out some of my other posts if you need more tips and info."

LG washer Burning Smell Service 7o7 4451591
How to Diagnose Drum Problems in Washing Machine
GE Washer Smoking During Spin Cycle

You have something between inner and outer tub remove top cover smell coming from air vents of outer tub then that is were it is
fun job its has to come all apart

THE INNER DRUM IS BAD WITCH LETS IT RUB THE FRONT SEAL OF THE WASHER YOU NEED TO SEE IF YOU CAN MOVE THE DRUM UP ARE DOWN ARE SIDE TO SIDE IF SO ONE OF THE SUPPORTS ON THE BACK BROKE AND THE GET THE SMELL OUT WASH THEM IN WHITE VINAGER

The motor could be leaking oil. Pull the machine out and look for stains or puddles on the floor.

call him soon

My Samsung washer has the same problem. Looking at it the gasket is being shredded by the drum and the rubber is burning. If it smells like burning rubber that is probably it. I do not know what caused this but I am going to just replace the gasket and see what happens

Sounds like seized . New could well be the next move .

http://www.devicemanuals.com/company/Indesit-manuals-page6.html
http://www.servicematters.com/maytag_library/docs/16022808.pdf
http://www.washerhelp.co.uk/washing-machine-repairs.html
Sounds like your clutch, or your motor, or belt, if there is one, has a problem, please use these service manuals to troubleshoot and hopefully isolate and repair your problem.

if it smell's like rubber it likley is .. smell's like a belt driven and it needs a replacment belt & idler .. remove the two screws at the bottom of front panel an remove .. in the front center at the bottom .is the motor / belt and pump .. if there is black rubber in bottom / wala . the belt is burning . / look for pump leakage / this would get belt wet and slip.. thanks mm .