WI: Dead Dudley. Effects on Elizabeth?

So, Robert Dudley dies before Elizabeth comes to the throne. Either of an illness he contracts in the Tower, illness more generally, or he gets killed alongside his brother at Saint Quentin.

What effect does this have on Elizabeth's reign? Power structures around the court will obviously be different. Is there any chance of Elizabeth being induced to marry, or would she remain staunchly disinclined to this?

Alternately, what if he gets assassinated during the early years of Elizabeth's reign (there were plots IOTL)? What are the results of this, other than Elizabeth getting pissed/sad/vengeful towards the perpetrators?
 
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