All eVar values sent to Adobe are stored, regardless of allocation. What allocation does is assign "credit" to the values for conversions (events).
So for example, let's say you pop eVar1 on every page view with a page name (and let's say the values are "page1", "page2", etc.). And let's say you trigger event2 when an exit link is triggered. Now let's say a visitor views 5 pages and then clicks an exit link. Then, you look at your eVar1 report using event2 as a dimension.
If eVar1 was set to Original Value, then you will see "page1" listed in your report.
If eVar1 was set to Most Recent, then you will see "page5" listed in your report.
If eVar1 was set to Linear, then you will see "page1","page2","page3","page4", and "page5" in your report.
But all instances are stored, yes. And you can also see all of the values if you were to throw the instances metric onto the same report (or use it as the only metric).
If you only want one value (the last value) to ever be sent to Adobe and referenced in any report, then you need to do that on a code level. Though in practice, it's not really possible/feasible to only trigger something on the last hit of a visit, as there's no real way to determine from a coding perspective which hit will be the last visitor activity.