Matthew 10:11

“And into whatever city or village you enter, search out who in it is worthy, and there stay until you go forth.”

This verse further explains the situation. They were going in the Name of the King. They should therefore expect provision of their needs by the King's subjects. Thus their very way of travelling in itself was to declare that the Kingly Rule of Heaven was now present. In each city or village they should therefore seek out ‘who in it was worthy'. This probably signified someone who had already demonstrated their worthiness by showing a responsive interest in the message of Jesus (there would be many such. But some would be prominently so as a result of their witness and their lives). Or it may be that they were to ask who it was in the town who was looked on as the most hospitable and godly. Such people would be the ones most likely to be open to their message. We can compare how in the Old Testament there were always the few who showed special hospitality towards strangers, even in the worst of places (e.g. Judges 19:16). But the principle was important. They were not to accept hospitality from just anyone, or look especially for the wealthy. They must rather seek to stay with someone of good reputation. Their acceptance by such a person would then enhance their own acceptability, and let all see that they were worthy men.

Once, however, they had been welcomed they were not later to move to somewhere else. They were to be satisfied with what God had first provided. Indeed to move on would in fact cause great offence and hurt. It would be an abuse of hospitality. If they found themselves turned out, of course, that would be a different matter. But that would presumably be a signal to move on (Matthew 10:23). However, if they had chosen well and prayerfully the hope would be that that would not happen.

There may also be the indication here that they were not to outstay their welcome. Once they had been in a place long enough for the original hospitality to have worn thin they should move on. Later, in the Didache (a late 1st century Christian writing) a Christian prophet would be judged by how long he stayed. If he stayed longer than three days it suggested that he was a sponger. That would not, of course, necessarily apply here, but it may bring out the principle in mind.