On the first page of the rules, in the callout box about conflicts between rules and cards, the first item on that list is:
Quote:
Originally Posted by The Rules
1. Nothing can reduce a player below Level 1, although card effects might reduce a player’s or a monster’s combat strength (p. 3) below 1.
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So, no, you can't get a Monster's (or player's) level below 1. However, Monster Enhancers, penalties, and the such don't change the Monster's (or player's) Level. They do affect combat strength (defined in the rules on page 3, as noted in that quote above), which can go negative.