How to remove baseboard installed behind hardwood floor?
A tool that may be very handy in this situation is an oscillating tool similar to this one:

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Not trying to promote any one brand, although the above shown is a good one, there are many brands to choose from. One thing to note is that there are universal blade types and then some manufacturers have their own blade holding design. Highly suggested to select an oscillating tool that uses the universal blade style.
With the wood saw blade that is about 1 1/2&quot; wide you can easily poke the blade and cut down at an angle into the space between the wall and hardwood floor to cut up the old molding into pieces. This should make removal far easier.
There are some blades that could be used to cut off nails as well. This could be handy for you to try to sneak the blade down behind the baseboard to cut off the nails flush with the wall. If you do use this strategy do note that quality blades for these tools are fairly pricey and nail cutting has a tendency to dull the blades much faster than when cutting just wood.