Dead *beat* means tired out to the maximum extent. A deadbeat (accent on 1st syllable) is someone who doesn't pay his debts. The difference is in the stressed syllable.

I think you're unlikely to mix these two up because context will usually give you the clue but you have come across an interesting and important thing within spoken English. We use stress to distinguish words. Sometimes, such as the example you gave, to distinguish the two words "dead beat" from the single word "deadbeat", and in other cases to distinguish a verb from a noun when they are otherwise identical, for example "REcord" from "reCORD". The first being a noun and the second a verb. In your example, "Deadbeat" would have a very clear stress on the first syllable whereas "dead beat" would have a roughly equal stress on each word. I hope this helps you.

I only know one meaning of deadbeat: “a person who does not pay his debts.” What other meaning are you thinking of?