The KM 2002 below is quoted in the Elder's book (with a 'paper-trail' through to 1978, as noted below) - so I presume is therefore still 'current'.
I believe it would be on the understanding that the child was living a generally 'moral' life at least when in the family home, and was not notoriously known by others to be living an 'immoral' life when outside the family life.
Also by saying "for a time" would indicate some kind of timeline for the child to get better and move out again from the family home. Of course, unfortunately, their are also situations when the mental/emotional and/or physical illness may also be a long-term or even life-long one, so it might need to be for an 'extended' time.
Kingdom Minstry, August 2002
Display Christian Loyalty When a Relative Is Disfellowshipped
The Watchtower addresses another situation that can arise: “What if a close relative, such as a son or a parent who does not live in the home, is disfellowshiped and subsequently wants to move back there? The family could decide what to do depending on the situation. For example, a disfellowshiped parent may be sick or no longer able to care for himself financially or physically. The Christian children have a Scriptural and moral obligation to assist. (1 Tim. 5:8) . . . What is done may depend on factors such as the parent’s true needs, his attitude and the regard the head of the household has for the spiritual welfare of the household.”—The Watchtower of September 15, 1981, pages 28-9.
As for a child, the same article continues: “Sometimes Christian parents have accepted back into the home for a time a disfellowshiped child who has become physically or emotionally ill. But in each case the parents can weigh the individual circumstances. Has a disfellowshiped son lived on his own, and is he now unable to do so? Or does he want to move back primarily because it would be an easier life? What about his morals and attitude? Will he bring ‘leaven’ into the home?—Gal. 5:9.”
Watchtower, September 15, 1981
If a Relative Is Disfellowshiped . . .
But what if a close relative, such as a son or a parent who does not live in the home, is disfellowshiped and subsequently wants to move back there? The family could decide what to do depending on the situation. [see footnote]
For example, a disfellowshiped parent may be sick or no longer able to care for himself financially or physically. The Christian children have a Scriptural and moral obligation to assist. (1 Tim. 5:8) Perhaps it seems necessary to bring the parent into the home, temporarily or permanently. Or it may appear advisable to arrange for care where there is medical personnel but where the parent would have to be visited. What is done may depend on factors such as the parent’s true needs, his attitude and the regard the head of the household has for the spiritual welfare of the household.
This could be true also with regard to a child who had left home but is now disfellowshiped or disassociated. Sometimes Christian parents have accepted back into the home for a time a disfellowshiped child who has become physically or emotionally ill. But in each case the parents can weigh the individual circumstances. Has a disfellowshiped son lived on his own, and is he now unable to do so? Or does he want to move back primarily because it would be an easier life? What about his morals and attitude? Will he bring “leaven” into the home?—Gal. 5:9.
In Jesus’ parable of the prodigal son, the father ran to meet and then accepted his returning son. The father, seeing the lad’s pitiful condition, responded with natural parental concern. We can note, though, that the son did not bring home harlots or come with a disposition to continue his sinful life in his father’s home. No, he expressed heartfelt repentance and evidently was determined to return to living a clean life.—Luke 15:11-32.
Footnote: Comments on the situation of elders and ministerial servants are presented in “Questions from Readers” in The Watchtower of February 1, 1978.
Watchtower, February 1, 1978
Questions From Readers: If children in the household of elders or ministerial servants come under a “charge of debauchery,” what determines whether the family head can continue to serve the congregation in an appointed capacity?
If gross wrongdoing by children in the household does raise serious questions in the congregation about a man’s presiding in a fine way over his family, he should not continue serving as an elder or as a ministerial servant. When the man serves as an elder and his fellow elders allow their judgment and decision to be swayed by friendship or sentimentality to the point of sidestepping Scriptural principles, then especially can his continuing to serve as an elder, though unqualified, be spiritually hurtful to the congregation. This is because it can undermine respect for the entire body of elders. It can provide an excuse for other children in the congregation to engage in wrongdoing. So, it is good to keep in mind that the man’s abilities as a speaker or an organizer or his likable personality are really not the point at issue. The determining factor is whether he is fulfilling his role as a father in a fine way. Only if he is may he continue to serve. Of course, when that is so, the body of elders should avoid being unduly critical and faultfinding in reviewing his family situation.