I know a little about this but certainly not all there is to know ...
A fiscal representative is legally responsible for all the debts and liabilities that could be incurred by property ownership. It could also include liability for personal debts where the home is the only asset and there is a penhora in place (A Lien against the property for those personal debts)
If for example a property is sold and capital gains tax not paid then at any point afterwards the government can retrieve it from the fiscal representative.
The fiscal representative is responsible for filing tax returns for the non resident he represents and for fines if they are late.
In any situation where money is due to the state and cannot be quickly or simple collected then the state has the ability to collect it from the fiscal rep.
You can certainly be Fiscal Rep for anyone you would wish, but why on earth would anyone want to take on that job?