Hi
@Thmeem,
I generally deal with individuals already in the asylum system in Germany or who have residency status here so I am not an expert on such cases. Here is my assessment of the situation:
If a person enters Germany and asks for asylum when checked by border control, then generally the border control is obliged to refer the person to the local reception center. The person would then be accommodated there and have their case heard in Germany.
However, the border control can refuse entry to a person if they believe another country is responsible for the person's asylum application. These rules are laid out in what is called the Dublin Regulation. This decides when a particular country is responisble for a particular asylum seeker's case.
If a person has an ongoing or rejected asylum case in Austria, or if Austria provided that person with a visa to enter Austria, then Austria would be considered responsible for any asylum claim the person makes.
Even if the person is allowed to enter Germany, register at a reception centre and make an asylum application, these Dublin rules are part of the asylum procedure and would be checked as part of the asylum prociess here. If it is determined that Austria is responsible for the case, the person would be told to return to Austira or potentially be deported there.
There are certain exceptions: if the person has a spouse or minor unacompanied children in Germany, it is possible for them to have their case heard in Germany.
The rules around the Dublin system are quite complicated and a local advisory service in Austria or Bavaria would be better informed than me about what the procedures are currently at the border. For example, in 2015 these rules were for a certain period of time suspended.
Here is more about the Dublin rules:
https://handbookgermany.de/en/rights-laws/asylum/dublin-procedure.html
Kind regards,
Éanna