I'm an asylum seeker living in Europe while my home country suddenly announced that "it will not renew or issue passports to anyone who's seeking asylum outside country". Does this fulfill the definition of statelessness ?
We are expecting a child anytime soon and in this scenario we wouldn't be able to transfer our nationality to child as we don't have passports and child's birth certificate couldn't be produced without passport. So where would the child be registered?
You're not technically stateless if your home country has not actually revoked your nationality. Passports and nationality are different things. Refusing to issue you a passport does not mean they are taking away your nationality. Countries are not obligated to facilitate their nationals' travel abroad. There are many situations in which people from some countries might be denied a passport from their country of nationality, including, for example, not having permission to exit, having unpaid child support or taxes, or children who do not have both parents' consent to travel, etc. In those cases, the person still has the nationality.
However, your lack of a passport while in a foreign country means you face many of the same issues that a stateless person would, like lack of proof of identity. Often, the procedures for stateless people will also apply to people who are not stateless but who are unable to obtain a passport. For example, many countries issue travel documents for people who are stateless or who are unable to obtain a passport from their country of nationality. If the country you are residing in offers one of those, you could try to get one.
I don't know what are the exact requirements to get a birth certificate in your particular country. It seems to me that a birth certificate is simply a record of the fact of the birth, and since the facts of the birth are not in dispute, they should be able to issue this record of birth regardless of your status or whether you have a passport. You should try to see how it is handled for children born to stateless parents, because those procedures probably also apply to parents who are unable to obtain a passport.
We are expecting a child anytime soon and in this scenario we wouldn't be able to transfer our nationality to child as we don't have passports and child's birth certificate couldn't be produced without passport. So where would the child be registered?
It depends on where you are. In the US, you would get the birth certificate from the county or city where the child is born, regardless of nationality (and the child would be a US citizen in addition to any other citizenship potentially acquired through you and the child's other parent).
As far as I'm aware, most places are similar: they issue birth certificates based on the place of birth, not the nationality of the child.
Whether the child obtains your nationality or the the nationality of the place of birth depend on the laws in those countries, as user102008 explains. It could be either, both, or neither.
If your child does not obtain the local nationality, and if you are unable to obtain a passport for the child, you may be able to get a "foreigner's travel document" of some sort. Details will be rather different depending on where you are.
You may also be able to get one of these for yourself, though I suspect that in most places you'll only be able to get one if your claim of asylum is successful, in which case it will be specifically a refugee travel document.
We are expecting a child anytime soon and in this scenario we wouldn't be able to transfer our nationality to child as we don't have passports and child's birth certificate couldn't be produced without passport. So where would the child be registered?
To add to the other two excellent answers, note that if you were actually stateless and unable to transfer your citizenship to your newborn child (which doesn't appear to be the case here), many countries have a fallback provision to immediately grant the local citizenship to the child. It would also typically apply to the children of unmarried mothers from countries that only allow citizenship to be inherited through men.
There are however exceptions. For example, in Europe, Austria was notorious for having no such provision. And obviously, countries that have unrestricted jus soli (including almost all of the Americas) do not need any special provision as a child born in this situation is generally a citizen.
