I think a lot of people underestimate the levels of movement in the past.
E.g. in 1890, 40% of Irish born people who were alive at the time lived abroad. Now, there were obviously specific social and economic circumstances which drove that, but 40% is still a huge proportion, and it doesn't even include those who moved area, but stayed in Ireland.
When I've looked at my family history, the amount of movement has really struck me. People requently moved away to where there was work, because there was no social safety net. Industries rose and fell, and populations moved with them.
Places like the US and Australia were populated by people who moved extremely far from where they were born (the slave trade obviously meant that many were forcibly transported, so I'm referring to those who chose to emigrate). Within the US, settlers moved thousands of miles as the west was gradually populated. The British Empire (and all the other empires) was administered by the people who moved overseas to run it.
Prior to the 20th century, even becoming a soldier or sailor meant that you basically left your family with no means of contacting them for months or years at a time. There were plenty of ways in which people quietly faded out of their family's lives.