When a housing bubble bursts, do rent prices decrease accordingly?

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I want to make sure when I'm buying rental properties, that they can remain profitable in any market. I ignore the possibility of the value of the property increasing,  I only am going to make decisions based on paying low enough for a property that'll give me my desired cash flow. 

However this can all go down the toilet if for some reason I buy at a good cash flowing price in a hot market,  then the bubble bursts and forces rent prices down and I'm not cash flowing anymore.  

I want to minimize my risk as much as possible, does anyone who has been affected in 2008 remember how much your rental income decreased in relation to your property value?

Thanks in advance.  I'm a beginner still trying to figure everything out so all insight and advice is appreciated.