A what stage should a person be evaluated to see if they need to be in a nursing home?

Your question is not clear. At what stage of What? should they be evaluated.

Nursing home care is the most expensive and the most restrictive so most patients go into nursing care when their condition has progressed to the point that it cannot be managed in any other type of facility. Obviously, most people do not go from home straight into a nursing home. There is usually at least one step between living independently at home and going into a nursing home, and that would be a crisis necessitating a hospital stay with a poor outcome.

The normal route is for people to go from living independently, to living with some in-home assistance, to assisted living or personal care, and finally into a nursing home. They would be assessed (evaluated) at each stage to see if there is some way of keeping them where they are without moving. Only when they really need more care than can be provided is the recommendation made to move into another level of care.

In the case of a dementing illness,the route into nursing care is less clear. There must be medical criteria for someone to go into a nursing care facility. Often patients with dementia are physically quite healthy. If there is a need for 'custodial' care because the person cannot be left unsupervised, sometimes that qualifies them for nursing care. Again, there should be an evaluation to see if placement in a less restrictive environment is possible.