[2020] Stalemate!

I don't know about the original poster, but I was inspired to recreate this state using the following deck:

Creature Spells: (3)

x1 Cult Guildmage

x1 Soulmender

x1 Kenrith, the Returned King

Non-creature Spells: (33)

x4 Lich's Mastery

x4 Chromatic Lantern

x4 Eyes Everywhere

x2 Role Reversal

x4 Liliana, Dreadhorde General

x4 Ritual of Soot

x4 Flame Sweep

x2 Chandra, Flame's Fury

x1 Chandra, Novice Pyromancer

x4 Ashiok, Dream Render

Lands: (24)

x4 Sulfur Falls

x3 Steam Vents

x4 Watery Grave

x4 Drowned Catacomb

x4 Blood Crypt

x3 Dragonskull Summit

x1 Reliquary Tower

x1 Memorial to War

Eyes Everywhere will exchange itself for any nonland permanent Sparky provides, giving them an all-important enchantment that you can exchange for Lich's Mastery via Role Reversal. (If Sparky is playing the green or white deck, you may be able to skip using Eyes Everywhere and exchange Lich's Mastery for their Gift of Paradise or Pacifism directly, for example.)

Once Sparky controls Lich's Mastery, you must avoid damaging Sparky at all costs, because there is a good chance Sparky will choose to sacrifice it and lose the game if you do. Instead, use Liliana, Dreadhorde General's ultimate ability to force Sparky to sacrifice all but one of each permanent type; typically this leaves one land, one creature, and one enchantment--Lich's Mastery!

From there, Memorial to War can destroy Sparky's very last land; Cult Guildmage can cause them to discard their hand; and Ashiok Dream Render can mill and exile their library and graveyard.

For extra staleness, Kenrith, the Returned King and Soul Mender can be used to make Sparky and your life totals match, while also helping you draw through your deck looking for any remaining combo pieces if you control Lich's Mastery. (The Chromatic Lanterns allow you to cast Kenrith, the Returned King and Soul Mender, and the Reliquary Tower allows you to skip discarding all those extra cards.)

Once Sparky has all cards in exile except for Lich's Mastery on the battlefield, you can then work on exiling all of your cards over the course of many turns by activating Chandra, Flame's Fury +1 ability to damage yourself while you also control a Lich's Mastery. Make sure you have an odd number of permanents available so that you, too, are left with only Lich's Mastery in the end! (Liliana, Dreadhorde General's +1 ability can help give you an odd number of permanents.)

Things to watch out for:

1. Almost every deck Sparky plays could destroy your single combo pieces (Kenrith, the Returned King; Soul Mender; Cult Guildmage). Wait to play these until after you lock Sparky out.
2. I have not encountered this, but if Sparky is playing the blue deck, they may be able to activate Eyes Everywhere to exchange it back for a nonland permanent you control!

Once you reach the stalemate, congratulations! You cannot outlast Sparky's patience and must eventually concede the match. Even with all cards in exile, you are always given a stop in your first main phase; this requires you to manually pass, thus preventing a runaway loop.