As far as I can tell from videos and the Wikia, nobody knows yet.
I would assume nothing, it just breaks the link and forces you to Special Summon in the Extra Zone again.
It would be way too broken if killing some 2300 ATK monster would kill all these XYz and Synchros on both
sides of the field just because they are unlinked now.
It did occur to me that there's a physical limit to link numbers, that being a Link 8.
There are only 8 possible markers, and you could never have a Link monster that used all 8 sides.
There's just nowhere on the field that would be possible.
Just becuase of the field limitations, I'd say Link 5 or 6s are the most likely major Link Monsters.
You're not going to typically get more than that in real play.
Even then with a 6 you're almost certainly counting a Link on your opponent's side since you need to
have a space to place the monster in your Main Monster Zone.
I imagine the 3 and 4s to be utilitarian, sort of relevant effect wise to Rank 4 Xyz Monsters or Level 4-6 Synchros.
Link 1 and 2s I picture as just throw away Link Monsters, basically just there to get your Xyz or Synchro out into the Main Zone
and maybe a cheap effect.
They'll probably be very weak and without Defense Position, your opponent will run them over the very next turn.
Maybe use them in cheeky ways to extend a Link because your higher Link Monsters didn't have the direction you needed.
Links, as I figure, will need advanced planning, because otherwise you could get yourself stuck with nowhere to Summon.
If you Summon a Link Monster that only goes left, but you've got more spaces to the right, you'll be stuck.
Also, it'll take more Extra Deck planning than just stuffing it with 15 OP cards.
The first Link Monster always needs one of the 3 down directions, otherwise you can only have the one.
Obversely, once you get to the Main Zones, if you can't go left or right, you're also in trouble.
You'll have to have a more strict plan in your head of the order you'll Summon Monsters.
I was thinking that you'll want more Link Monsters in your Extra Deck than Fusion, Synchro, or Xyz just to have options
in case your opponent Summons a Link Monster before you. A way to take advantage of that in addition to your own.
Konami really has set it up now to where something like the old fashioned Elemental Heros can't be played.
To have more than 1 Fusion on the field, you'd need at least 2 Link Monsters on the field, leaving you only 1 space for
anything from your hand.
Sorry for the essay, but I've been having nonstop thoughts on this now that I comprehend it.
What I do like is that this turns Pendulums from spam city to more of a utility that baically feeds your field Link Monster materials.
Pendulum Zones, when you have them, prevents you from playing too many Traps or Continuous Spells,
so you really can't be as effiecient with Pendulum focused decks anymore.
These new Link mechanics really are going to change everything if you think about it.
It's not like previous where it all still sort of worked like classic Yu-Gi-Oh, just regularly getting faster.
I feel like the focus of the game will shift from OP effect spam to more of a control-based game.
Also, Senet cards might actually be relevant since Linking depends highly on card position!