Asking a complete stranger for a subreview for a conference?

I am a CS guy and can answer this question.

Yes of course. That is what conference chairs do perhaps. As you told the person has already published in past conferences like this. If some researcher is active in the field of his/her research arena and agreeing to review the manuscript. This is what is called peer-review. My recommendation would be to contact the researchers through academic e-mail ids of theirs to make it more transparent.

In my experience it may make sense to send subreviews out for people who are junior than you and you know that they can replace your particular expertise (e.g. your postdocs, possibly senior PhD students). Note that you are responsible for their reviews in this case. Otherwise, unless you are a Scientific Committee Chair, it is not strictly your job to select reviewers, or you would have been asked to do that in the first place.

I personally do not give out subreviews for precisely this reason - if I am editor, or in the scientific committee (which selects reviewers), of course, I do select reviewers, and that's what my job description is; but when I am asked to review, I assume they want me and my expertise and not some variation of me. However, some conferences explicitly permit subreviewers, so it really depends on the situation.

In any case, I probably would consider a subreview to be directly your responsibility, so if the subreviewer messes up, it's your job to fix it - or if it is contentious, but not questioned by you, to defend the review.