I usually say that, in English, the comma is almost always optional, even though many English teachers prefer to say they're required, probably to make things simple for their students. Commas mirror the pauses that occur when a sentence is spoken out loud, and different people will put pauses in different places.
That being said, if you're going to set off an independent clause with commas, you have to use the second comma if you use the first comma. Otherwise it looks weird. For example:
The horse, standing by that tall man is named Sylvester.
You can see how this punctuation is confusing as the pacing of the sentence is awkward. As a glance we might wonder whether the horse or the man is named Sylvester, because it's not clear whether "standing by that tall man" is meant to be an independent clause.
Either of these are fine, although the commas do make it easier to read:
The horse standing by that tall man is named Sylvester.
The horse, standing by that tall man, is named Sylvester.
It's slightly awkward but not particularly confusing, to just use the second comma:
The horse standing by that tall man, is named Sylvester.