Tomorrow they would say: "Sorry, man. Your client just doesn't have segwit-data. We also can not provide it to you, but we are sure that it exists somewhere so we will not reorganize the main chain."
Pedantically, that isn't how the protocol works. You cannot transfer the block without segwit data to supporting full node systems. Older systems don't get it, but it doesn't matter if they get it or not as they wouldn't enforce any rules with it. I think your question is actually about old systems, in which case the transmission part is a distraction.
The segwit data is not sent separately.
Why? One
can send block to the network to all nodes 0.12.x, 0.11.x etc, wait 30 seconds, and send the segwit data
Old software indeed doesn't necessarily verify all the rules that are at play: this is unavoidable, since you cannot even know potentially all the rules that are at play as miners could be enforcing ones no one but they know about. The same holds for any rule addition, like P2SH, or CLTV, or CSV.
At least for intentional public rule additions, the process limits exposure: In the BIP9 protocol no new rules are added until two weeks after 95% of hashpower signals an intent to enforce. During that time and before full node software will have been producing loud warnings: "Warning: Unknown block versions being mined! It's possible unknown rules are in effect", "unknown new rules are about to activate", and "Warning: unknown new rules activated", notices for a month-- allowing parties to upgrade or connect their node via another upgraded node (that filters the blocks they receive). The process also is date gated to give time for upgrades even before it potentially begins. No non-upgraded full node software will create addresses using the new rules (nor would any prudent wallet generate them until they're widely enforced in the network) nor accept unconfirmed transactions that use them as they're non-standard. One could set their wallet to automatically delay or withhold action when a new rule they haven't been updated for has gone into effect, until upgraded or manually bypassed for that particular new rule, but for virtually any application that would be excessive-- considering that 95% of hashpower are updated to enforce and a process which results in wide deployment of node software.
(As an aside, segwit would be in 0.12.2/0.12.3; and potentially 0.11.x too though it looks like there isn't demand for it)