Welcome to the Wefugees community and thank you for reaching out to the community with your question.
In general, Article 18 of the European Unions Charter of Fundamental Rights grants people a right to asylum.
The following explanation is from a UK legal aid site, but it applies to other EU countries:
"What is asylum?
If someone is at risk of being persecuted in their own country, they may go abroad and ask for asylum in another country. Granting ‘asylum’ means giving someone permission to remain in another country because of that risk of persecution.
In legal terms, a person who has asked for asylum in the UK and is waiting for a decision on that claim is called an asylum seeker. Someone who has received a positive decision on his or her asylum claim is called a refugee.
Although some asylum seekers might enter the UK illegally, once they have applied for asylum they are no longer ‘illegal’. Anyone seeking protection is entitled to stay in the UK while awaiting a decision on their asylum claim.
The right to claim asylum is in international law. Governments are obliged to provide protection to people who meet the criteria for asylum. The UK has signed these international laws and they are part of UK legislation."
Since the Dublin III Regulations came into effect, the first EU- country that registers your fingerprints, issues you a visa, or where you have applied for asylum is responsible for your asylum case (if any of this applies, you can't claim asylum in another EU-country, even if you withdraw your asylum or the case has been rejected. There is more information about Dublin cases here on our platform).
This article from Deutsche Welle describes How to apply for asylum in Germany.
"How will my status in Germany be determined?
Whether you can stay in Germany long-term depends on the outcome of the asylum application process.
To kick this process off, you need to register as an asylum seeker at an initial reception facility. Then you can apply for asylum.
The only place to do this is at your local branch of the Federal Office for Migration and Refugees (BAMF).
In an interview, you will then have to explain why you fled your country and why you cannot or don't want to return. Your reasons are recorded in writing. Those who don't speak German will get a translator."
Also have a look at this Welcome to Europe site: you can find out more about asylum procedures in many EU countries. Follow this link.
If you do not have any passport, you are entitled to a "Grey passport". Please see the following threads for more information on who is entitled to a Grey passport (especially the first one, please scroll down to find Nilab's answer).
Do I need the passport in orderto get the residence permit?
Do I qualify for a "Grey Passport"?
I hope these sources help to understand your rights and asylum proceedings in the EU better.
Please feel free to reach out to the community again if you need any further assistance!
All the best,