I’ve heard that people bring food to the house of one sitting shivah. What food or other gift is appropriate to bring or to send?
Strictly speaking, we are not allowed to give gifts to mourners because this is something done on happy occasions, and the purpose of Shiva is to talk about, and remember, the deceased, and all the good deeds he/she did. Something like a gift could distract the mourner from this essential process of coming to terms with their loss while in the company of loved ones and friends.
But food is a different story. There is a special mitzvah for neighbors/friends to bring food to the mourner’s home for the first meal after returning from the funeral. This meal is called the seudas havra’ah. While this is the only meal others are required to provide for the mourner, it is a widely practiced custom that others provide meals for the mourner throughout shiva. Since mourners are overwhelmed by feelings and thoughts, it is a mitzvah to take the responsibility of preparing meals off of their shoulders. This is not a gift, but rather an act of kindness.
May G-d bring us all only joyous occasions,
Shlomo Shulman