I wouldn't take over a rotisserie chicken -- when my brother passed, we received, no lie, almost 20 chickens. It was crazy! I guess everyone is trying to think what to deliver, aside from lasagna.
If you want to send something truly unique, send items for breakfast. You can pre-bake scones and freeze them, or make freezer biscuits that they can bake as needed. Then include a big container of plain yoghurt and a bag of granola, maybe some fresh berries, but not too many. You want to give them things that will keep in the fridge or freezer.
Banana bread (or muffins) zucchini bread, blueberry muffins, strawberry bread, raisin bran muffins, etc. all freeze well and make great afternoon snacks too.
Jars of soup, mild chili or corn chowder are always good for lunch or dinner. If you put the soup hot into canning jars, they'll create a simple "seal" while cooling, to help them stay fresh longer. Otherwise, you can put them into freezer bags and freeze before delivering. Soups with rice and beans freeze really well, like turkey wild rice, navy bean, or lentil with sausage, etc. But I'd avoid pasta, as it turns to mush. You can also freeze mini baguettes and add a hunk of cheese to serve with the soup. Both will keep forever if they get overwhelmed with fresh food they need to eat straight away.