DB gebrauchtzug

No, you can buy and own a train as a private person.

There is one person in Berlin, who owns a steam train and has it parked in his garden.

[https://www.eisenbahn-museumsfahrzeuge.de/index.php/deutschland/staatsbahnfahrzeuge/dampflokomotiven/baureihe-80/80-009](https://www.eisenbahn-museumsfahrzeuge.de/index.php/deutschland/staatsbahnfahrzeuge/dampflokomotiven/baureihe-80/80-009)

Technically, you can buy and own a train as a private customer, but putting it in your garden can be costly. The advertised train types are S-Bahnen from 99/2000, so probably not too interesting from a historical standpoint yet. It’s most likely that they will be bought by a foreign train operator.

I think that if you have a large enough private property, you can run your own private railway system. Themeparks sometimes have them, e.g. the FEZ in Berlin.