A Simple Question on Permanence

[TPFKAP]

This is a thought experiment.

Tomorrow morning, a vaccine is announced which is highly available and which provides effective immortality.
Anybody who wants the vaccine can have it without cost or judgement and therefore will live forever.
The vaccine halts the ageing process and removes all disease and entropy, but does not protect from external physical harm.

For the purposes of this experiment, sexual reproduction is also rendered obsolete.
Anybody who elects not to become an immortal being on this plane will die a natural death and will not be replaced.
There are however tightly controlled methods of asexual reproduction which will only ever maintain the population at a number equal to the number which initially elected to live forever.

The question is:

How would this alteration affect approaches to "permanent" methods currently used to address actions such as murder - assuming the current approach is the death penalty or life in prison; is an infinite amount of time long enough to reform every circumstance?

Everything just slows down forever anyway, so I would say yes.