Okay, here. I went through every assassin and specialist. Here's a list of talents and abilities that can give the vast majority sustain and defense. Out of all of them, I counted only seven lacking any form of HP sustain. If you don't have any supports, try some of these out! Some are better than others, but they're there!
Abathur: Rarely on the front line, but is considered a sustain hero and can talent to heal allies with Regenerative Microbes
Alarak: Innate healing off Lightning Surge, Sustaining Power to increase it
Azmodan: Gluttony, Gluttonous Ward
The Butcher: Innate healing with Butcher's Brand, multiple talents to increase both that and in-lane sustain
Cassia: Ring of the Leech, Plate of the Whale
Gall: Attached to a warrior
Chromie: No innante sustain, does have long range
Falstad: Hammer Gains, multiple talents and abilities to grant temporary shields
Gazlowe: Goblin Repairs
Genji: No real sustain
Gul'dan: Drain Life in base kit, multiple talents to increase that and also Healthstone
Illidan: Innate life steal on basic attacks, multiple talents to buff it
Jaina: No real sustain
Kael'thas: Fel Infusion talent grants heal on trait use
Kerrigan: Trait grants temporary shields, Assimilation Mastery increases regen while shielded. Siphoning Impact heals on Ravage kills
Li-Ming: Dominance restores health on takedowns, Diamond Skin grants temporary shield after Teleport
Lost Viking: Trait grants increased health regen with globes collected
Lunara: Siphoning Toxin
Medivh: Innate shielding ability, Reabsorption adds heal
Murky: Rejuvenating Bubble, Egg Shell
Nazeebo: Hexed Crawlers, Blood Ritual
Nova: No real sustain
Probius: No real sustain, can gain shields from talents
Ragnaros: Empower Sulfuras heals in base kit. Catching Fire, Cauterize Wounds, Tempered Flame, Submerge
Raynor: Adrenaline Rush is heal in base kit that can be buffed with talents. Vigorous Assault
Samuro: No real sustain
Sgt. Hammer: Regeneration Master, Vigorous Assault, First Aid
Sylvanas: Life Drain
Thrall: Trait heals on ability use, can be increased via talents
Tracer: Is That a Health Pack?!, Leeching Rounds, Total Recall
Tychus: That's the Stuff!
Valeera: No real sustain
Valla: Siphoning Arrow, Tempered By Discipline
Xul: Harvest Vitality, Rathma's Blessing
Zagara: Nydus Network, Hydralisk Transfusion
Zeratul: Shroud of Adun, Mending Strikes
Zul'jin: Regeneration in base kit, can be improved through talents.