Forced to do so.... by what?
WA,
Some examples (specific to inside my house):
1) Refusal by a person who seems to comprehend his actions to leave my premises - I may back to a point of cover/concealment tactically, but I don't believe in "retreat" within my home as a moral necessity, period. This doesn't mean I'll automatically shoot, but it does mean I'll challenge from a position of strength. (If at all possible, the lady will have called 911 while backing to a position of safety with her preferred handgun; NOBODY is getting past me to where she will be without being given cause to regret it.) If a person who otherwise appears coherent insists on closing with a homeowner who has told him to depart, that suggests that he thinks I am not a threat, which tells me that he is.
2) If the person seems obviously out of touch with reality, I'll try to maintain distance, but again nobody gets near the lady of the house, so I will only back up so far. If no weapons are apparent, and if the person isn't ridiculously large, then non-lethal options may be pursued once I've reached my limit. I'm on the large side, wrestled for a few years and have studied aikido for a dozen years or so. I have pretty decent odds of taking down the average person without having to inflict a lot of damage.
However, I've had friends get shot by people they had not thought dangerous - if the person acts like he has a weapon and intends to use it, I won't wait to see what is drawn from concealment, so hopefully there won't be any suspicious motions. The suggestion of a weapon draw will immediately escalate my response, sane or not.
3) If the person immediately gets violent, I'm not playing. If an unarmed attack, good odds I'll just take them down. However, if armed or of such a size and demeanor that I'm not positive I can handle them via non-lethal means, they get shot until hostile action ceases.
4) As previously caveated, short of the person being obviously drunk, or blatantly psychotic or schizoid in demeanor, or just bewildered looking, it's going to be hard under adrenalized, short distance, time critical conditions to decide the person is mentally off.
Non-violent people who don't close distance will be reasonably safe. Non-violent people who do close distance will probably be taken down, if they don't seem overwhelming. Violent people will be engaged, sane or not.