It very much depends on the owner/manager of the property.
We're staying in a time share at Disney (less than a week!!!) and they provide all towels, linens and basic kitchen supplies (ex food). I think they provide one dishwasher packet. We are taking ~ food ~ some special cooking items (muffin tins, a casserole dish) ~ dish soap ~ laundry supplies ~ night lights ~ paper towels ~ toilet paper ~ dishwasher detergent.
When we rent a house at the beach, we also have to supply our own towels (incl dish towels), pillows and sheets (sometimes they provide pillows, usually they have blankets or comforters for beds), and some more cleaning supplies like ~ lysol ~ toilet paper ~ trash bags. It's not unusual to arrive to find no toilet paper, no tissues, no paper towels - NOTHING except furniture, basic cooking supplies, and tvs. I personally hate that. I always make sure to leave a roll in each bathroom and paper towels on the counter.
But I always get a list of what's included in the rental before we go. Since we usually drive, I bring my most of my own dry goods, linens and paper products with me, and I buy meat, produce, dairy products, etc when we get there. If we are going with a large group, we only bring one day's dry goods plus paper goods, then we brainstorm our meals for the week and send out a shopping expedition. Be aware that in some beach communities, you may drive 30 minutes or more to find groceries (Outer Banks is notorious for this).