For a homicide
to be considered justifiable in the eyes of the law
the situation must be proven to fulfill certain requisites. These requisites vary from country to country but mainly revolve around establishing that there was a clear and present danger
to one's life or limb
or to that of an innocent person, and the only way to have stopped this danger was to inflict deadly force
These are what constitutes clear and present danger:
- The attacker's ability to inflict bodily harm.
- A plausible motive for the attacker to inflict bodily harm.
- The lack of alternatives or obvious impossibility of withdrawal or retreat.
These are just the bare basics, if ever confronted with a threat and you are mentally weighing if it is a shoot or no-shoot situation, keep in mind the preceding requisites. Fail to prove any single one of these and you can count on being charged with manslaughter or even murder and getting your ass hauled off to jail.
Notice that this only covers threat to one's life or limb, the threat to property is a different thing altogether. In some countries, there is a "castle doctrine" saying that anybody who breaks and enters into your property can be legally met with deadly force.
Though this does somehow encourage people to include their property in the things they are allowed to protect with deadly force, it is, in general, not justifiable to shoot somebody who snatched something from you and is now running away. Exit wounds in the frontal area of the person does not make for a very good case unfortunately.
Do not take this as legal advice as I am not a lawyer.