According to Wikipedia
Computer scientists consider a language \"type-safe\" if it does not allow operations or conversions that violate the rules of the
Many programmers will equate static type checking to type-safety:
Sadly, it's not that simple.
For example, C and C++ are not type-safe because you can undermine the type-system via Type punning. Also, the C/C++ language specifications extensively allow undefined behaviour (UB) rather than explicitly handling errors and this has become the source of security exploits such as the stack smashing exploit and the format string attack. Such exploits shouldn't be possible in type-safe languages. Early versions of Java had a type bug with its Generics that proved it is was not completely type-safe.
Still today, for programming languages like Python, Java, C++, ... it's hard to show that these languages are completely type-safe because it requires a mathematical proof. These languages are massive and compilers/interpreters have bugs that are continually being reported and getting fixed.
[ Wikipedia ] Many languages, on the other hand, are too big for human-generated type safety proofs, as they often require checking thousands of cases. .... certain errors may occur at run-time due to bugs in the implementation, or in linked libraries written in other languages; such errors could render a given implementation type unsafe in certain circumstances.
Type safety and type systems, while applicable to real-world programming have their roots and definitions coming from academia – and so a formal definition of what exactly is "type safety" comes with difficulty – especially when talking about real programming languages used in the real world. Academics like to mathematically (formally) define tiny programming languages called toy languages. Only for these languages is it possible to show formally that they are type-safe (and prove they the operations are logically correct).
[ Wikipedia ] Type safety is usually a requirement for any toy language proposed in academic programming language research
For example, academics struggled to prove Java is type-safe, so they created a smaller version called Featherweight Java and proved in a paper that it is type-safe. Similarly, this Ph.D. paper by Christopher Lyon Anderson took a subset of Javascript, called it JS0 and proved it was type-safe.
It's practically assumed proper languages like python, java, c++ are not completely type-safe because they are so large. It's so easy for a tiny bug to slip through the cracks that would undermine the type system.
References: http://www.pl-enthusiast.net/2014/08/05/type-safety/ and https://en.wikipedia.org/wiki/Type_system