Let's phrase the question a little differently:

If gold were running out,
and you owned a gold mine,

Wouldn't YOU start looking for something "better"?

Give up the gold laden bank,
and start mining for silver?

in terms of replacing gold with a shinier metal, more beautiful, one that doesn't decay.  there's no other metal that can replace gold.  silver is not a better replacement.  it is a distant second.  but then again, people don't need gold to drive a car, get groceries, make fertilizers, power light bulbs, etc...  i've got paper money has replaced gold.

but not so for oil.  there is no one thing that replaces oil.  i've had this debate numerous times with my stupid friends.  stupid because they can never get past the one stone-cold fact - there is no replacement for oil and because our world is so dependent on it, we're oh so screwed.

so if a abiotic oil person dares to step to me about peak oil, i'll bust out the - what is wrong with you!  humanity has yet to figure out how to replace oil, therefore, the oil companies are just gonna ride it out with fingers crossed.

It was a joke.

The point is that if YOU are in that lucky, catbird's position, you mostly sit back and watch your gold mine become more and more valuable over time.

Then, when you are good and ready, and the price of gold is high enough for your liking, you start selling some in exchange for other stuff you may want.

So same answer if you are sitting on an oil well and do not have a need to immediately pump out everything in it. Your only threat is if someone comes along and claims they have a cheap alternative to gold (or oil). If they do, they are a threat to your "wealth". To preserve your wealth, you need to debunk them or otherwise put them out of their misery.

This is simply the "Invisible Hand" weaving its magic solution for the good of all of us. Got it?