Here are two potential workflows I would like to perform in a web application.
Variation 1
Things are simple in the application layer - every request is served by a different thread (or process), so unless you have state in your processing classes (services), everything is safe.
Things get more complicated when you reach the database - i.e. where the state is held. There you need transactions to ensure that everything is ok.
Transactions have a set of properties - ACID, that "guarantee database transactions are processed reliably".