I guess it depends on what you mean by valid syntax.
You could design a language that accepted any string but ignored anything that had not been prescribed specific meaning. This is basically the equivalent of saying "I'll get rid of syntax errors but saying they're not errors" - pretty pointless and hugely undesirable for many reasons.
Beyond that the only way you could have a language which had no syntax errors would be to have every possible string have a valid instruction / use associated with it. The only way I can see to do that would be to have all operations as single characters and to ensure that every single character had an operation assigned to it.
There are a million things wrong with this - obviously there are no reserved words, it's all about where it's used in context and as a result it would be basically illegible and, while immune from syntax errors would be far more likely to experience every other sort of error.
So theoretically possible (AmmoQ puts it far more neatly than I) but entirely undesirable.