you do sometimes get firmware upgrades for ECUs from manufacturers, however these are pretty much only ever done on a recall / service item basis, usually to fix bugs or errors in ECU programs.
you sometimes find they are a recall item and people are called in to have their ECU reflashed - probably for a safety reason.
other times some bugs will be fixed and it is important but not enough to warrent a recall, so this will be done free with the next service or should someone present at a dealer reporting specific issues that an ECU re-write will solve.
you are almost certainly never going to find a software upgrade just for the sake of upgrade, if there isnt any massive or important issues there is no want for anyone upgrading their ECUs.
if it is required it will only ever be a dealer level function, never trust anyone else other than a dealer offering to upgrade firmware, you want it from a trusted source. its typically done through dealer only software, in Fiat ARUK case EXAMINER.
1999 156 1.8TS Sport Pack 3
2001 166 3.0 V6 24V Super
2003 156 GTA 3.2 V6 24V
2005 156 1.9 JTDM-Jet Sport
2008 159 1.9 JTDM Lusso
1997 GTV 2.0TS Lusso
2001 147 1.6TS Lusso