So a creature with damage equal to or greater than its toughness marked on it dies when state-based actions are checked. Damage is not removed until the cleanup step. This means that a creature that is damaged and has its toughness changed to 1 will die barring anything else that changes this situation.
Now I have a different question; what happens if I have something in play that makes my creatures +1/+1, like Thistledown Liege? Does the creature (mine) still become a 0/1?
Now I have a different question; what happens if I have something in play that makes my creatures +1/+1, like Thistledown Liege? Does the creature (mine) still become a 0/1?
Ovinize makes the targeted creature have "base power and toughness 0/1" (C.R. 108.1, 613.3b). Any applicable effects of the form "get[s] +N/+M" or "get[s] -N/-M" (such as found in Thistledown Liege) are still applied to that creature and modify its power and/or toughness accordingly (C.R. 613.3c, 613.4). See also this thread.
It will still get the buffs that would apply to it from th liege. If it was a white (or blue) creature, it will be an 0/1 and get +1/+1 so a 1/2, if it is both white and blue it will get +2/+2 and be a 2/3, Ovinize just changes the creatures base stats, if it has an enchantment or equipment boosting its' stats they still get boosted.
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Commander: UBG Tasigur, the lab enabler UR Planeswalker Control UBRW Breya's personal box of combos BRW Vampire beats, by Dre 1 Karn, where all lands are command towers UBR Inalla's Venser lock UBRGW Atog Atog contraption tribal WUB Xur's second chance UGW Derivi, bird tribal R Brother's Yamazaki BRG Prosh, the scourge of multiplayer GW Capt. Sisay's Deck Dumping Service UB All Your Spells do Belong to Me UG Tapioca Pearl BG Meren's grinder
I̟̥͍̠ͅn̩͉̣͍̬͚ͅ ̬̬͖t̯̹̞̺͖͓̯̤h̘͍̬e͙̯͈̖̼̮ ̭̬f̺̲̲̪i͙͉̟̩̰r̪̝͚͈̝̥͍̝̲s̼̻͇̘̳͔ͅt̲̺̳̗̜̪̙ ̳̺̥̻͚̗ͅm̜̜̟̰͈͓͎͇o̝̖̮̝͇m̯̻̞̼̫̗͓̤e̩̯̬̮̩n͎̱̪̲̹͖t͇̖s̰̮ͅ,̤̲͙̻̭̻̯̹̰ ̖t̫̙̺̯͖͚̯ͅh͙̯̦̳̗̰̟e͖̪͉̼̯ ̪͕g̞̣͔a̗̦t̬̬͓͙̫̖̭̻e̩̻̯ ̜̖̦̖̤̭͙̬t̞̹̥̪͎͉ͅo͕͚͍͇̲͇͓̺ ̭̬͙͈̣̻t͈͍͙͓̫̖͙̩h̪̬̖̙e̗͈ ̗̬̟̞̺̤͉̯ͅa̦̯͚̙̜̮f͉͙̲̣̞̼t̪̤̞̣͚e̲͉̳̥r͇̪̙͚͓l̥̞̞͎̹̯̹ͅi͓̬f̮̥̬̞͈ͅe͎ ̟̩̤̳̠̯̩̯o̮̘̲p̟͚̣̞͉͓e͍̩̣n͔̼͕͚̜e̬̱d̼̘͎̖̹͍̮̠,͖̺̭̱̮ ̣̲͖̬̪̭̥a̪͚n̟̲̝̤̤̞̗d̘̱̗͇̮͕̳͕͔ ͖̞͉͎t̹̙͎h̰̱͉̗e̪̞̱̝̹̩ͅ ̠̱̩̭̦p̯̙e͓o̳͚̰̯̺̱̰͔̘p̬͎̱̣̼̩͇l̗̟̖͚̠e̱͉͔̱̦̬̟̙ ̖͚̪͔̼̦w̺̖̤̱e͖̗̻̦͓̖̘̜r̭̥e͔̹̫̱͕̦̰͕ ̗͔̠p̠̗͍͍̱̳̠r̰͔͎̰o͉̥͓̰͚̥s̟͚̹̱͔̣t͉̙̳̖͖̪̮r̥̘̥͙̹a͉̟̫̟̳̠̟̭t͈̜̰͈͎e̞̣̭̲̬ ͚̗̯̟͙i͍͖̰̘̦͖͉ṇ̮̻̯̦̲̩͍ ̦̮͚̫̤t͉͖̫͕ͅͅh͙̮̻̘̣̮̼e͕̺ ͙l͕̠͎̰̥i̲͓͉̲g̫̳̟͈͇̖h̠̦̖t͓̯͎̗ ̳̪̘̟̙̩̦o̫̲f̙͔̰̙̠ ̹̪̗͇̯t͖̼̼͉͖̬h̹͇̩e͚̖̺̤͉̹͕̪ ͚͓̭̝̺G͎̗̯̩o̫̯̮̟̮̳̘d̜̲͙̠-̩̳̯̲̗̜P̹̘̥͉̝h͍͈̗̖̝ͅa͍̗̮̼̗r̜̖͇̙̺a̭̺͔̞̳͈o̪̣͓̯̬͙̯̰̗h̖̦͈̥̯͔.͇̣̙̝
UBG Tasigur, the lab enabler UR Planeswalker Control
UBRW Breya's personal box of combos BRW Vampire beats, by Dre
1 Karn, where all lands are command towers UBR Inalla's Venser lock
UBRGW Atog Atog contraption tribal WUB Xur's second chance
UGW Derivi, bird tribal R Brother's Yamazaki
BRG Prosh, the scourge of multiplayer GW Capt. Sisay's Deck Dumping Service
UB All Your Spells do Belong to Me UG Tapioca Pearl
BG Meren's grinder