Learn Russian: Пропажу обнаружил хозяин. - The missing item was discovered by the owner.

This is a classic example of Russian putting the new or most important information (the focus or Rheme) at the end. We already knew something was missing (the Theme, Пропажу), but the new fact is exactly who found it. English often uses the passive voice to get this same emphasis at the end of the sentence.

Since Пропажу is at the beginning, how do we know it is not the subject?

The ending -у tells us that пропажа is in the accusative case, making it the direct object. The word хозяин is in the nominative case, so it must be the subject. Russian uses cases rather than word order to show who is doing the action.

What exactly does Пропажу mean here? Does it mean the act of losing or the missing item itself?

The noun пропажа can mean both the event of losing something (the disappearance) and the missing item itself. Depending on the broader context, the owner either discovered that something had gone missing, or they found the actual lost item.

How would the meaning change if I used the standard word order and said Хозяин обнаружил пропажу?

That standard Subject-Verb-Object order just tells a simple story: 'The owner discovered the loss.' By flipping it to put хозяин at the end, the original sentence specifically answers the implicit question 'Who discovered the loss?' rather than 'What did the owner do?'