Somebody stayed behind.
Their family kept going too.

The half that goes missing

One person left. A whole family didn't.

Emigration usually took one or two people out of a household, not all of it. Often a young man went first, and the land, the house and the parents stayed with a sibling. Within one generation the two halves of the family stopped writing to each other. Letters got fewer, someone died, an address was lost, and after that nobody on either side knew the other existed.

So when people say "we have no family over there", what they usually mean is "we lost track". Those are very different things. The first is a fact about history. The second is a gap in the paperwork, and paperwork gaps can sometimes be closed.

It is also the most personal reason to look. A name on a baptism record is history. A second cousin who still lives a few houses from where your great-grandfather was born is family.

Where the siblings are written down

The same books that hold your ancestor hold his brothers and sisters

A parish register does not care who emigrated. Every child born in the house was baptised and written down, often with the house number beside the name. When a brother married, the marriage went into the book. When his children were born, they went in too. Once you have found your ancestor's own baptism, you are already looking at the page where his siblings will appear.

That is how the line is followed forward. From the parents to every child they had, from each child who stayed to the person they married and the children they had, and so on through the generations, as long as the books survive. It is slow, careful work, because the same first names repeat in every family and the spelling of the surname drifts with each priest, the same way it did on the American side.

Sometimes the books also explain why the families lost each other: an early death, a farm that passed to one heir, a sister who married away and took her husband's name. The silence between the two branches usually has a reason, and it is often on the page.

How close to the present it can get

The archive goes quiet about a century back, and that's on purpose

Old registers end up in state archives, and many of them can be read. The recent ones cannot, at least not freely. In Poland, for example, civil registry offices keep birth records for 100 years and marriage and death records for 80 before handing them to the archives, and while they are still at the office, access is generally limited to close family or someone they authorise. Other countries in the region have rules of their own. Either way, the books protect living people, which is fair.

So the archive can usually carry the sibling lines into the early twentieth century, close to the people who would be alive today, and then it stops. The last stretch is crossed in other ways: a surname still common in the village, a parish that still exists, a DNA match that suddenly makes sense once you know which branch it belongs to. None of those is guaranteed. But they work far better when you already know exactly which family, which house and which village you are looking for.