The so-called "liquid facelift" is use of one or several injectable fillers (Restylane, Perlane, Juvederm Ultra, Juvederm Ultra Plus, Radiesse and others, though these are the most common) in conjunction with Botox or Dysport (muscle paralytics helpful in reducing dynamic skin wrinkles, but not static ones) to restore facial volume, reduce wrinkles, and provide some degree of facial rejuvenation. If you don't have much skin laxity or sagging, and your lines aren't too deep or severe, then you can have nice results from the "liquid facelift." But of course, if all you need are these relatively minor improvements, then you didn't really qualify for the more dramatic and visible changes achievable via surgical facelift. So, as with most things, you get what you pay for. If you really need a facelift, a "liquid facelift" will only make slight improvements or delay the need for more aggressive surgical intervention--it will never replace a well-performed surgical facelift!
As to safety--any surgical procedure has risks, but so does driving a car, or doing virtually any kind of activity. True, these risks are minimal--we drive to work or play each and every day, usually without problem. Yet, over 35,000 people die each year in traffic accidents in the US, with nearly 3 billion miles driven, so this is rare when taken in context of the risk per mile driven. Facelift surgery is serious surgery, which is why you should seek a well-trained, experienced, board-certified surgeon who operates in an accredited facility with well-trained, experienced, certified anesthesia providers. The risk of any complication is low if you adhere to the above advice and follow your surgeon's recommendations.