Do any people live e.g. in Romania and work in Hungary?

There might be some tax issues which give you an advantage.

However, there is virtually nothing on the Romanian side of the border. The Eastern part of the country of Hungary is not very well developed and border areas in Romania are not industrialised. For example, there are no worthwhile airports in Hungary but there are some in Romania. As usual in pre- and post-Communism, the focus is on the capital. There are Romanian speaking peoples in Hungary living on the border but there are less Hungarian speakers in Romania (more concentrated in Erdely - aka Transylvania). However, Romanian is very easy to learn if you know French, Italian or similar. Given a preference, I doubt anyone would chose Romania over Hungary. The situation is not comparable to say commuters living in France and travelling on a daily basis to Geneva (in Switzerland).

The Western side of Hungary is more commuter land but many people speak good German in the Western border areas rather than English. In my opinion, Austrians are not as good in languages as Hungarians so German is essential. In Budapest, every educated younger person is speaking at least some English and not so much German. Austria is oriented almost entirely towards Germany itself and Switzerland.  A lot of Hungarians commute to Austria from Sopron (as do Slovakians from Bratislava). Salaries are higher in Austria than in Hungary which is an incentive. However, the work seems to be mainly oriented to service industries.

Sources: 2 years living on and off in Romania, 7 years living in Austria close to the Hungarian border and many years of involvement in Hungary overall!