Sometimes, a member of the pack falls out of favor with the pack.

For example, this could be the sister of the alpha female or some other low ranking individual. The alpha female only tolerates her through the groveling the individual does to keep in favor. Sometimes this alone is not enough, and the individual can be driven from the pack.

This wolf then becomes a lone wolf, who has no pack. This is very dangerous for that wolf, as it is more difficult to get food without the pack. It is also in danger from other packs that will attack it if it strays into their territory.

Lone wolves only become a member of a pack if they are fortunate enough to find a pack that will accept them, or alternatively find a mate of its own who is in the same predicament, and start a pack of their own. Those lone wolves that do this are better off. Since they start a pack of their own, then they are the alpha themselves.