It is my understanding that passports belong to the government that issued them. Good rule of thumb here in the DR is to never voluntarily surrender your passport to an "nonlegal entity". If somehow you are separated from your passport and know who has it, you can call your embassy and they will get it back for you. There may still be a legal block against you leaving the country but most people or businesses are not allowed to seize your passport without judicial authorization; Even then the Govt will be the one asking for it not the moto rental place or a local hospital.
Right,
Only a JUDGE(not a fiscal or such) can order that you have to give in your passport, so you can not leave the country to flee your responsibilities, a bill etc.
And even then, he asks you to do so, you can deny, which means you go to preventional jail then until your case is settled or trialed.
No other institution has the right to keep your passport.