It's complicated. Those that came here to do low paying jobs (pre-Brexit) do not contribute more over their lifetime compared to the average person born here, they contribute less.
But those on average or high wages do contribute more - largely because we haven't paid to educate them and raise them. So there are not those costs.
A number of people here have been saying "Who's going to do all the rubbish jobs that we won't do?"
Well, increasingly, it's going to be people born here.
With the exception of some jobs like care home workers and nurses who can be employed on lower wages, anyone who wants to come to work in the UK (with the exception of seasonal work eg on farms) has to be paid a minimum of £38,700.
For context, the median salary for a full time employee in the UK is £37,430.
If you want to be a dustbin person (refuse collector) you are not going to be paid anywhere near that amount. I just checked and Hull council are advertising for this role and paying up to £25,854 per year.
An immigrant could not come here and work as a refuse collector.
There are lower salary limits for care home workers, nurses and some other jobs. The exceptions to the general rule include job roles like nuclear scientists (but only in Scotland), archaeologists, lab technicians, professional dancers, orchestral musicians, graphic designers, jobs in the fishing industry, horse racing grooms and work riders.
Then there are a lot of construction roles; stonemasons, bricklayers, roofers, carpenters & joiners, welders.
If an immigrant has one of these skills then they do not have to be paid the higher figure of £38,700.
If they don't have one of these skills then they need to have a job which pays at least that much.
There are other routes. For example, recent graduates under the age of 26 have lower limits or those with a PhD in a STEM subject.
But, generally speaking, the era of immigrants coming here and doing the very low paid jobs (apart from seasonal farm labouring) is very much over.