Auxiliary belt pulley FIAT Doblo Estate (119_, 223_)

The auxiliary belt pulley that fell out below your FIAT Doblo Estate (119, 223) and has a broken rubber ring between an outer and inner metal ring is very likely an idler or tensioner pulley. This type of pulley typically includes a rubber damping element to reduce noise and vibration, and a failure like a broken rubber ring would cause rattling before complete failure.

In your vehicle, the auxiliary (serpentine) belt runs over pulleys for various components including the alternator, power steering pump, and also passes over tensioner and idler pulleys. The pulley that failed is not usually part of the alternator or power steering pump itself but a separate pulley designed to guide or tension the belt.

From repair guides and replacement tutorials for FIAT Doblo 1.3 and 1.9 (119, 223), there are usually at least two pulleys involved besides the main accessory pulleys:
- The tensioner pulley (spring-loaded) that keeps the belt tight,
- And one or more idler pulleys which guide or route the belt.

The rubber damping ring you describe fits the design of an idler or tensioner pulley bearing, which uses a rubber element between metal parts to absorb shocks and reduce noise.

Given that the power steering and charging (alternator) have stopped working while the belt is still in place, it indicates the belt lost proper tension or alignment, very likely due to the failed pulley.

What you should do:
- Replace the entire pulley (likely an idler or tensioner pulley) as a unit. Do not try to repair the rubber ring.
- Inspect the tensioner condition as well, since failure of one pulley can affect belt tension.
- It is beneficial to replace the auxiliary belt at the same time if it shows wear.
- Parts are listed as "Drive belt tensioner pulley" or "idler pulley" for FIAT Doblo 119, 223.
- These pulleys are aftermarket available and can be ordered as OEM or quality aftermarket brands.

In summary:
The failed pulley you describe is almost certainly an idler or tensioner pulley from the auxiliary belt system, not directly the power steering pump or alternator pulley itself. The broken rubber between inner and outer rings points to bearing damping failure inside that pulley. You will need to replace this pulley to fix the rattling, restore belt tension, and get power steering and charging back.

For accurate part ordering and replacement instructions, checking the tensioner and idler pulleys for your FIAT Doblo 119 or 223 model year and engine variant is recommended. If unsure, a mechanic familiar with Fiat belt systems can quickly identify and replace the correct pulley.