In part, however, this was possible for him because it wasn't clear that his alleged US crime would have been a crime under Icelandic law so extradition from Iceland wasn't an issue. Fischer died in Iceland in 2008 having successfully evaded US capture as a fugitive for the last 16 years of his life.
However what Fischer managed as recently as 2008 would be significantly more difficult today. In part Fischer got by through the use of a Swiss bank account in which he deposited millions of dollars in assets.
Because of something called FATCA (the Foreign Account Tax Compliance Act) as well as some direct prosecutions of Swiss banks, Swiss bank secrecy--especially for US citizens or those born in the US--is largely a thing of the past.
Even if you have another passport, if it shows a US birthplace a bank (anywhere in the world) is required to (and will) send the person's details to the US IRS.
It is an open question whether the IRS would then share that data with other three letter agencies (like DHS or FBI) to assist in an extradition--but in general it is fair to assume that the trend is that it is getting much harder to hide from Uncle Sam anywhere in the world. The data transfers contemplated by FATCA started only in Sept 2015 so this is a fairly recent development.