It depends on the ticket you bought them. If you've been sensible, and bought them a CIV ticket from your origin to London International (more details from the man in Seat 61), then the CIV protections extend back to your original starting point. In that case, if anything delays you on your way to St Pancras, be that your train or the underground, then CIV protections kick in. No matter your ticket, Eurostar will (after verifying the problem) rebook you for free on the next train with seats that you can make. (Normal checkin times apply, as you exchange you ticket in the ticket office before security). If there's epic #fail, and you end up missing the last Eurostar of the night due to the delay, then they'll even sort out out a hotel for free.
If you were a bit of a muppet, and didn't buy a CIV ticket (they're normally cheaper! as they don't tend to have peak restrictions), then you fall back on Eurostar's generally great customer service. If you were delayed for a reason that's clearly not your fault, and if you've left yourself lots of time, they will normally (within some limits) take pity, and rebook you for free on the next available service with seats. If you're taking the piss, then they might stick to the rules, and ask you to pay a fare difference and change fee. Officially, they stick to the rules, but in practice if you've been delayed by an inbound train and left yourself lots of time before, they'll rebook you (and have me a few times)
However... You're probably fine. At a normal walking pace, it takes just under an hour to walk from Liverpool Street to Kings Cross / St Pancras. Eurostar checkin for most people closes 30 minutes before departure (10 mins for Carte Blanche and Business Premier customers). So, you've time to walk it, and stop for a refreshing cold drink part way.
Outside of peak times, you'll find a bus for at least some of the route, and tube tickets + NR tube transfer tickets are valid on buses on reasonable routes during the strike. Taxis can be had if you want one, with a queue that'll be fairly long, but well under an hour.
Other options include walking to Farringdon (20-30 mins), then taking a Thameslink train to St Pancras low-level (5 mins walk to Eurostar checkin), or the slightly crazy and will-cost-extra option of a 5 minutes walk to Morgate, Great Northern to Finsbury Park, Great Northern back south to Kings Cross, then walk over the road to St Pancras (5 mins walk to Eurostar checkin)