Contrary to popular belief, most introverts can in fact do things like engage in small talk, introduce themselves to a stranger, or meander about within a crowd. (Though we do prefer when it is a controlled, purposeful crowd as opposed to a mob, that is certain.) We are just not as comfortable or in the very least, not as inclined to do such things. They are outside of our status quo. Yet if we find that by doing so a greater good is achieved, we will undertake such actions. But the stakes have to be much higher for an introvert than they have to be for an extrovert.
For example one would hope that even the most reclusive introvert would save a stranger from drowning if they came across such a scene and could help. Yes they have to touch and communicate with someone they don't know, and in normal circumstances they are not thrilled about that. But saving a life makes it the highest of stakes. This is of course an extreme example, but the point is that an introvert is far less likely than an extrovert to take an action or to make a comment simply because they can. It's rare that I quote Star Trek movies, but in this case think of Mr. Spock after saving Kirk who has just fallen off a mountain:
"Perhaps 'because it is there' is not sufficient reason for climbing a mountain."
The "sufficient reason" will of course vary from introvert to introvert, but you can bet in 90% of cases there is one. That is why we don't speak much at meetings; we are weighing if there is sufficient reason to bring up the point we are formulating. That is why we don't usually seek to be the center of attention; we have determined there is not sufficient reason to halt to proceedings in order to be observed. Introverts need a sufficient reason before they go out on the town or attend a party with mostly strangers.
And yes sufficient reasons for all of these things can be found for the introvert. We may attend a party for the sake of one person we care about. Perhaps we have determined we need a break from our own thoughts, and go out on the town. We may even attend a networking event, if the event is designed specifically with writer's or other creatives in mind. So long as the stakes weigh more than the uncomfortable action, introverts will do it in most cases. But you can bet a week's pay that they have made that determination before they have taken the action.
And the stakes must be higher than "getting out there". Often, even appealing to an introvert's self interest is not raising the stakes high enough, because an introvert tends to be more motivated by ideas and creativity, and less by personal gain.
Extroverts on the other hand tend to drive meetings, offer all their half-formed ideas, enjoy having everyone look at them and listen to them, and can't wait to get away from themselves and get out on the town, or to the next party. At which they will thrive on talking to strangers. And even if they don't make a single friend or establish one single toe-hold somewhere, (though they usually do), the extrovert is ready to go out the very next day and do it all again, because the stakes of not doing so are too high for them.
So if you want to motivate an introvert to say something or to do something, don't just encourage them to "come out of their shell" or to "join the party". That doesn't tend to move us. But if you can take a few extra moments to determine what the stakes are, and have the patience and willingness to present them to an introvert in a respectful way, you may find them more willing to partake. Especially if you present to them a problem that you feel can be solved with their participation.
If you are an introvert, how high do the stakes have to be for you to do the "extroverted" stuff? Can they ever be high enough?