‘Open borders’ is a strawman, anyway. You can have policies which promote immigration, provide legal pathways for immigrants to provide labor to the economy (including unpaid labor like raising kids and domestic elder care), and can structure social benefits in such a way that you provide a social safety net, without having to just throw the border open to all or pay out unemployment benefits to anyone who shows up out of work.
Illegal immigration is a market response to a failure of the government to provide a legal framework for sufficient legal migration. People are willing to come to (for example) the US and work illegally without legal access to any social safety net. But allowing people to live under those conditions is both a moral failing (we should not be comfortable relying on the labor of people who face destitution if they lose their job) and a societal risk (people with no safety net are more likely to end up engaged in criminal activity that harms society).
So why not create a more structured arrangement? Create paths to legal immigration, with access to defined, limited, temporary benefits, and with a pathway that over time - as an immigrant’s stake in the country increases - converges towards the full security afforded to citizens.