Myetherwallet is safe unless you have given your private key or you have been phished. Always be careful when you enter your credentials because it might not be the correct site. When you receive e-mails from sites, always check if it is the true site because there are many hackers who would send e-mails saying you need to change password because someone is trying to access your account. If you have slack, do not ever open the e-mails saying you need to update your myetherwallet because it is just a phishing site. If possible, bookmark the site you are using so that you don't need to search it in google. Most likely the first one that would appear when you search is an advertisement and a phishing site.