Citizens typically enjoy the best human rights protection of anyone in the territory of a country, relatively speaking. Even in badly governed states or dictatorships they are better off than immigrants, legal or illegal. And also in perfect democracies do citizens enjoy more rights than legal immigrants: the former have political rights, the latter do not. See this post for more information about this difference.
However, in a perfect democracy, legal immigrants and citizens enjoy the same level of protection with regard to all other types of rights, non-political rights such as freedom rights. This is called the principle of constitutional universality.
Illegal immigrants of course have a much harder time, even in perfect democracies. As they live in the “dark” they will find it difficult to come forward to complain about rights violations or to go to the police or the judge. Doing so will reveal their illegal status and will result in forcible return to their country of origin.
Asylum seekers or refugees have an even harder time because they are usually imprisoned for the duration of their asylum application. And as they are imprisoned, they usually find it difficult to escape into illegality when their application is denied. Compared to normal illegal immigrants, the government knows where they are – in prison – and hence can easily return them to their own country.
The worst off are the modern slaves. Many of them end up in slavery as a consequence of migration and trafficking, but not all. Many modern slaves are normal citizens.
Since citizens generally enjoy the best rights protection, it is a good strategy for non-citizens to try to become citizens. Traditionally, only legal immigrants can apply for citizenship (when some conditions are fulfilled). Asylum seekers, when their application is accepted, become legal immigrants and then they can, in the next step, try to apply for citizenship. If their asylum application is rejected, they are either send back or disappear into illegality. Together with other illegal immigrants, they first have to become legal immigrants (for example through some kind of amnesty measure) before they can hope to apply for citizenship.