Opening a store while one of the owners is sitting shiva; a matter of loss
Question
Two partners own a store, and one of them is sitting shiva. Is it permissible for the second partner to open the store in a case where they have losses because they do not open the store, such as payment to workers who do not come to work, and also the rent that they pay for the store and the like?
Answer
One should not open a store publicly even when there is a matter of loss; the custom is to be lenient to open from the fourth day onwards.
Source
Aruch HaShulchan, Yoreh Deah, Chapter 380, sections 26 and 27: 'They ruled in the Tur and Shulchan Aruch section 21 that two partners who are shopkeepers, if one of them experiences a bereavement, they close their shop so that the partner won’t sell publicly, but he can sell privately in his house even if he sells for both partners. But if the mourner is an important person and the partnership is named after him, and even if his partner will sell privately in his house, it will be known that the mourner has a part in it, it is forbidden for the second partner to sell even in his house. And it seems clear that this does not make a difference even if this is a matter of loss, because only labor itself was permitted to the mourner if it’s a matter of loss, as explained, but the prohibition of working in public was not revoked because of a matter of loss. And according to this, what we permitted in business dealings, is only the sale or purchase in a matter of loss in his house, which is private, but not in a store, which is public, and the proof of this is that we do not even worry about the partner's loss for this reason, how much more so we do not worry about his own loss.'
And he wrote that one should judge favorably those who are lenient, who hold that it is permitted to work publicly if it’s a matter of loss. In practice he concluded that one should not be lenient in this.
However, after three days, it was clarified in Chachmat Adam that the custom has spread that they were lenient. And so it is written in Mishnah Berurah 548:24.