Imagine the cops are looking for a criminal. That criminal is hiding but not for long in one place. He is changing places all over the world and continuously hiding . What is the correct word or phrasal verb for this? "The criminal is roaming worldwide" is wrong I believe as this sentence would mean that he is on a happy vacation seeing places. So, what is the correct word? Please advise.
On the run
Edward Snowden was on the run from the US government after leaking NSA documents.
This is the more modern way of saying on the lam.
I don't think there's any one-word way to say this. "On the lam" is OK but pretty dated (1930s). "The criminal is staying undercover and roaming worldwide" is long but fairly racy and idiomatic. If you want it to be even more raacy, change "criminal" to "perp" (cop-talk for "perpetrator").
to go to ground OED
fig. (of a person), to withdraw from public notice and live quietly or ‘lie low’.
the literal is of a hunted fox ... ducking underground.
As in your example:
"The criminal is roaming worldwide, unseen, having gone to ground."
1964 Ann. Reg. 1963 326 The four men ‘went to ground’, probably in Johannesburg.
From Longman's go to ground: B(BrE)
to make it hard for people to find you
wherever you are, usually for a long while.