Why is こと used at the end of this kind of sentences?

Question

So, often I see こと being used at the end of sentences like

「私の最後の希望はあなたと共に死ねることなのに」

「それは僕の生命を吸い取るために　僕の全身を凍らせていないことだ」

Is this like how in English you normally would say "My aim is ーーー" and you would use a verb in gerund form like "living there" (although to live there would be ok too)? So because 希望 is a noun what 希望 is should be a noun too, therefore 「死ねること」is like "My hope is dying with you", right?

Should the second phrase be understood as:

それは•••全身を凍らせていないことだ
That is... not freezing my whole body

Would this phrases make sense without こと?

Answer 1

Your understanding is basically correct, this こと is a nominalizer, something that turns a verb into a noun. You need a noun before だ, なのに, etc.

• What is the difference between the nominalizers こと and の?
• Wasabi - Nominalizers: こと and の

But note that 死ねる is the potential form of 死ぬ. Thus 死ぬこと is "dying" but 死ねること is "being able to die". Likewise, 凍らせていない is negative -teiru form. 凍らせないこと is "not freezing" but 凍らせていないこと is "having not frozen".

私の最後の希望はあなたと共に死ねることなのに
My last hope is being able to die with you, but...

それは僕の生命を吸い取るために　僕の全身を凍らせていないことだ
It is that [something/someone] has not frozen my whole body in order to absorb my life.