FIFPro said the players, who it described as "trapped", would be able to take advantage of a change to an insolvency law which has until now treated them as assets of clubs in financial difficulties.
This means they have not been able to join a new team without the permission of their club's administrators even when they have not been paid.
FIFPro quoted the Romanian players' union AFAN as saying the new legislation would affect around 300 footballers at 14 cash-strapped first and second division clubs, including top sides such as Rapid Bucharest and CFR Cluj.
World Cup
Did Ronaldo wrongly claim Portugal goal or did he touch it?
AFAN legal advisor Aurora Dohatcu said that, from Friday, players who have not been paid for three months would be able to file an application with the Romanian football federation (FRF) and would be free to leave within one month.
"We are receiving a lot of calls from players who want to leave clubs," Dohatcu said. "Some of them have given us power of attorney to represent them."
Dohatcu estimated that 50 footballers might try to leave immediately because of the law change, FIFPro said.
Many of the remaining 250 unpaid players at the 14 clubs could choose to stay on in the hope that management would turn around their financial situation, she said.
AFAN president Emilian Hulubei and general secretary Dumitru Costin led the challenge to change the law by lobbying politicians and publicising the plight of players, FIFPro said.
FIFPro has often said that, away from the elite clubs, many players in Europe struggle to be paid on time and are often ostracised by their clubs if they complain.
Punishments can include making them train on their own, often at unsocial hours.
Last year, seven Romanian top flight clubs had points deducted by the FRF for failing to put their financial affairs in order and meet licensing criteria
World Cup
'Horrendous' - Cole says 'no way' Portugal should have got penalty for handball
The Emirates FA Cup
Man City v Chelsea, Man Utd v Everton in FA Cup third round