A campaign is a legal entity that officially makes all of the financial transactions for the candidate. Campaigns are non-profit corporations and are regulated by the FEC.

This type of campaign can be "suspended" because it literally exists in the real world. A suspended campaign means that the candidate dropped out but the campaign hasn't been formally dissolved yet by the FEC.

For example:

John Glen's 1984 presidential campaign did not officially end until 2006 because it owed $2 million in debt. He had to continuously file FEC reports during that time, but he wasn't secretly plotting to reenter the race.

The word "campaign" can also mean "a connected series of operations designed to bring about a particular result". This type of campaign is more like a mood or a feeling. It exists in the hearts and minds of a candidate's supporters. However, it does not actually exist in the real world and can't be suspended.