In a case like this, use either two commas or none:
The boy, whose pen was lost, was very poor.
The boy whose pen was lost was very poor.
In this case, I think you should use two. Here's how one comma usage guide explains it:
3. Use commas to offset appositives from the rest of the sentence.
Appositives act as synonyms for a juxtaposed word or phrase. If the appositive occurs in the middle of the sentence, both sides of the phrase need a comma. As in, "A mallard, a kind of duck, attacked me."
There's one exception to this rule. Don't offset a phrase that gives necessary information to the sentence. Usually, commas surround a non-essential clause or phrase. For example, "The duck that attacked me scared my friend" doesn't require any commas. Even though the phrase "that attacked me" describes "the duck," it provides essential information to the sentence.
So, in your sentence, I would use two commas. However, if we change the sentence just a little bit, we might decide to use no commas at all:
The man whose fortune was lost was now destitute.
The Purdue Online Writing Lab has more information about punctuation.