I was told that last year the Prophet Russell M Nelson and the brethren declared an end to the home teaching practice the way we had known it. Why do my former home teaches still want to come over at the same time to my house every month?
Although it is true that the “Home Teaching” program has been discontinued, the need to care for the Lord’s sheep has not been abolished. The program is called “ministering” and it is similar to Home Teaching program intended to care for the members in each separate ward and/or branch.
Each household in the ward or branch will have ministering brothers—priesthood brethren—to minister to and care for the individual or family. Every adult sister will have ministering sisters—members of the Relief Society and possibly the Young Women as well—to minister to and care for her.
Ministering assignments will be provided by leaders, who will meet with ministering brothers and sisters—preferably as companionships—to counsel about the strengths, needs, and challenges of those to whom they minister.
You can read more about this change following this link.