You’ll seldom see that used with a comma to set off a non-restrictive clause. Normally which does this job. (Which is also fine in restrictive clauses, by the way, despite the pseudo-rule that forbids it. The first link explains the terminology.)
My earlier post on non-restrictive that gives an idea of how rare it is, and provides an ambiguous example from Penelope Fitzgerald; I later updated with more clearcut literary examples. This post notes a few more instances of non-restrictive that used in books I recently read and re-read, respectively.
In Everest: Impossible Victory, Peter Habeler writes:
The men struck their Camp VI at 8200 metres, that is well below the place at which Mallory and Irvine were last seen.
And Marshall McLuhan, in Understanding Media:
The rapid increase of traffic brought in the railway, that accommodated a more specialized form of wheel than the road.
The wheel, that began as extended feet, took a great evolutionary step into the movie theatre.
Habeler’s line is ambiguous: that could either be a relative pronoun (or perhaps a subordinator), used where we would expect to see which; or it could be a demonstrative, which means there’s a comma splice where we would expect a dash or full stop.
You could argue the same for the first McLuhan line, but you’d be on even shakier grounds, I think. My feeling is that these thats are non-restrictive relativizers. I’d be curious to know how you read them.