We will not be loosing our gil but that does not mean that our gil will not potentially lose its value in the change-over. 2.0 is going to bring with it a massive change in game play as well as how the game is organized and seeking to establish an even playing field in terms of the in game economy is certainly something I can see SE attempting to do.
This sort of thing happens all the time when MMOs release new expansions. Players simply find themselves having more gil on hand then they ever did before simply by participating in new quests/content. In this specific case the advent of a more quest based level up system could inject a huge amount of disposable gil into the economy. Instanced dungeons could also have this effect.
If you want to hold on to the value of your hard earned gil the safest bet would be to invest in an item or set of items that you believe will hold its value in the changeover (anything related to the relic quest is probably a safe bet). The value of an item will always fluctuate in both directions but the value of your gil will likely only ever go down. Once the storm is over, but your stuff up for sale at the newly settled price and reap in the inflated profits. This is a tactic that works very well even for patches as well (especially considering the new recipes in big patches get released before the servers go down).
When all is said and done, past all the whining and moaning that changes like these things cause, this sort of thing is actually very healthy for the community in the long run. It ensures that an even playing field is established once every few years. Of course, those who care about making gil as efficiently as possible will always find themselves on top of the economy in the end anyway but still it creates an opportunity to obtain virtual wealth for newcomers where one may not have existed before.
For those that are skeptical about this sort of thing, hold on to that skepticism until we can confirm whether or not the gil cap changes in 2.0. If it gets any higher then expect and prepare for a very very large amount of inflation.