In the timeline within the fiction where time travel was discovered, the decay quickly dispatched most of humanity. Six people banded together along with those that followed them.

From the rider mail in THD14:

"Stardate 1982: just a little joke. Research proceedes as planned on the Chrono Temporal Flux Fusion Engine. We were encouraged when a rice cake appeared in the machine's primary servo dock informing us that several minutes later we would succeed in transporting a rice cake backwards in time. This is a step forward as we previously have only been able to transport inorganic matter. Dwayne and I celebrated with drinks and a viewing of Blade Runner. Rutger Hauer's final speech is brilliant, especially five drinks in. Tomorrow we plan to attempt to transport a living insect, our first test of a live specimen. Wish us luck!"

From the business card collected at GDC2016 by Liz English:

"They arrived at dusk. The experiments had been wildly successfu[l], more so than we could have hoped or feared. At first, we welc[o]med them. The people of Tunisia are friendly and, [g]enerally, we expected that our vis[i]tors would treat us with the same wonder and amazement with which we regarded them. That could [n]ot have been further from the truth. They did not care about our presence, or lives, or [c]ities, or us. They went about their brutal business as if we were ants in their path: with a comp[l]ete disregard for our [e]xistence. Their capability for warfare thwarted our greatest weaponry, and their unearthly abilities countered the strategies of our greatest [m]ilitary and scientific leaders. As the d[e]cay radiated out like a cancer from the Tunisia[n] coast, those in power around the world watched in helple[s]sness, knowing that soon their nations would suffer the same fate as ours. There are at this [p]oint in history fe[w] of us remaining. Those who survived have banded [t]ogether [u]nder the guidance of we origi[n]al six, though at this point only four remain. Our numbers are smaller by the day, and our enemy has all but forgotten us. Their victory was total, an[d] our defeat pushed ou[r] species to the brink of extinction. We now resist the decay. We hide. We w[a]it. And we plan. -Excerpt from An Oral History of the Decay, Interview 8674-B"

From the message hidden in the source code from the party lounge:

"This seems like a secure place to hide information, so here goes: watch out!  You may be using this Party Lounge to take your mind off of the grueling reality outside this base.  You may be secure in your position as a high-ranking resistance officer. Be warned: danger lurks in even the safest of places.  Do you know what relationship Numbers 1, 3, 5 and 6 have to the decay?  Have you never wondered what happened to Numbers 2 and 4?  Have you questioned the abductions of individuals from prior eras, or the futures you are trying to prevent?  Stay alert.  I'll be in touch as I am able, but do not look for me - it may be some time until my next communication is able to get through to you."