I don't know what you are playing against exactly. It isn't even possible for Warlocks to play 8 minions with Lifesteal in Standard (outside of discovers), but maybe you mean cards with soul fragments. Or you mean Demon Hunter. But either way, none of them are legendary or epic cards, and the only "unfair" epic or legendary related to this mechanic (and respective decks) I can think of would be Soulciologist Malicia.
Assuming that your deck just doesn't work against the opponents you are facing, you might need to switch to a different deck, but for that it's important to know what exactly you struggle with. Could you perhaps be more specific which cards you keep seeing that give you so much trouble?
I also don't know how many games you've played or what your expectations are. Just to give you an idea, it's not unusual to lose 5+ games in a row on a bad day. It sure sucks when it happens, but that can (and does) happen to everyone.
It seems you are under the impression that the right legendaries or epics are absolutely necessary to win, but that is plain wrong. You most certainly can win with a small collection and budget decks. Not as frequent perhaps, but it is definitely possible. And I doubt, without knowing your collection, that you are factually unable to make a deck that can win. Though as others have pointed out before, how you play is also important.
Even in the absolute worst case, you'll get access to the full core set in a few weeks, with plenty of good cards in it. However bad your collection is, you will get some strong cards soon enough.
As for rank floors: That is right, if you are stuck on a rank floor, you can't drop anymore. But honestly, it really doesn't mean much. It's not like you can get to Silver 5 by accident and then all your opponents are way too good for you. The difference between ranks is not that big for the most part. Even if you stumbled somehow into Platinum or Diamond, you can still win games with suboptimal decks. If you have a Star Bonus left, it's a bit different though.
I don't know what you are playing against exactly. It isn't even possible for Warlocks to play 8 minions with Lifesteal in Standard (outside of discovers), but maybe you mean cards with soul fragments. Or you mean Demon Hunter. But either way, none of them are legendary or epic cards, and the only "unfair" epic or legendary related to this mechanic (and respective decks) I can think of would be Soulciologist Malicia.
Assuming that your deck just doesn't work against the opponents you are facing, you might need to switch to a different deck, but for that it's important to know what exactly you struggle with. Could you perhaps be more specific which cards you keep seeing that give you so much trouble?
I also don't know how many games you've played or what your expectations are. Just to give you an idea, it's not unusual to lose 5+ games in a row on a bad day. It sure sucks when it happens, but that can (and does) happen to everyone.
It seems you are under the impression that the right legendaries or epics are absolutely necessary to win, but that is plain wrong. You most certainly can win with a small collection and budget decks. Not as frequent perhaps, but it is definitely possible. And I doubt, without knowing your collection, that you are factually unable to make a deck that can win. Though as others have pointed out before, how you play is also important.
Even in the absolute worst case, you'll get access to the full core set in a few weeks, with plenty of good cards in it. However bad your collection is, you will get some strong cards soon enough.
As for rank floors: That is right, if you are stuck on a rank floor, you can't drop anymore. But honestly, it really doesn't mean much. It's not like you can get to Silver 5 by accident and then all your opponents are way too good for you. The difference between ranks is not that big for the most part. Even if you stumbled somehow into Platinum or Diamond, you can still win games with suboptimal decks. If you have a Star Bonus left, it's a bit different though.