Having worked on dryers more times than I care to count I can attest to the fact that it is not only possible that they may escape through the dryer; they are actually induced to make the attempt because the very design of the dryer invites such activities. I have seen socks, coins, paper money, sundry items such as paperclips, small toys and yes I have even seen a hanger or two manage to make a getaway. The drum is fixed to a short motor shaft at the rear of the dryer. The front of the drum is not actually attached to the dryer. The front of the dryer has a handful of slightly curved tab like projections that find themselves inside the drum when the front of the dryer is assembled. The seal is also attached to the front of the dryer and wears out as time goes by. This allows the drum to float to some degree rather than being fixed to something. It is through these seemingly doubtful gaps that the socks make good their escape. It usually starts with the occasional sock finding its way out. As the dryer ages the number (and size) of the items that escape increases until finally, you guessed it; mass exodus.
In most cases the escapees make things worse as they will usually find themselves outside the drum ( therefore beyond the sight and reach of their human masters ) but trapped within the dryer itself. That part of their bold journey is fraught with danger and disappointment. Especially if it is a gas dryer. I have found them in the dryer duct. Perhaps this is an indication that some of their counterparts actually made it outside the dwelling. I doubt that I will ever know because they are no where to be seen ( although I have heard stories ). In any event if you notice that you are losing large numbers of socks it is time to have the local technician or your otherwise useless brother-in-law run routine maintenance on the dryer. This will increase the efficiency of the dryer, prevent the machine from wearing out altogether and in the case of a gas dryer or situation where air flow has been severely obstructed by the bodies of unsuccessful escapees the routine maintenance may very well prevent a fire. It may also prevent the number of escapees from rising to the point that they feel confident about returning to rescue their fellows that were left behind.