Yes, Magento has server side validation for some forms. However, the module that added the form is responsible for checking it - therefore, if you are dealing with third-party code, such as a plug-in, it may be missing.
Typically, the verification code contains part of the module model. For example, in the Magento built-in analysis function, when submitting a review form, its data is checked by the validate() function in the file /app/code/core/Mage/Review/Model/Review.php . I would start by looking at this code and the code in existing Mage / Core modules for examples.
In the situation you give, the usual place for the validation logic would be /app/code/local/YourCompany/PriceNotify/Model/Pricenotify.php
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