In reference to the patent: US8516220
The broader claims of patent US7644114 include the idea described int the later patent.
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I am not an expert in this field, but if you look at the first claims you will see that the '114 patent specifies a first and second backup page with a dirty flag for each. The '220 patent specifies only one page with a bit for indicating dirty status and two extra bits. So although the application seems similar, the actual implementations seem to be different.
The '220 patent has 12 prior patents and applications cited by the examiner as prior art. The '114 patent is not one of them so it is possible it was overlooked by the examiner.
As to your question whether the '220 patent is merely as specialization of the '114 patent, I'm not skilled enough in the field to say. Even if it were, so long as the specialization was sufficiently novel and non-obvious, there is no reason why the patent shouldn't be granted. This doesn't mean that it can be practiced without assessing infringement on the '114 patent first (or any other relevant prior art).
The '114 patent status (according to the USPTO's Public PAIR system) is "Patent Expired Due to NonPayment of Maintenance Fees Under 37 CFR 1.362". 7/8/2005 is the priority date for this patent's parent application (according to PAIR).
It looks like the priority date of the '220 patent is 11/5/2010. I haven't compared the '114 to the '220, but the '114 is prior art to the '220, so if the claims of the '220 patent are anticipated by the '114 patent, the validity of the '220 can be challenged based on the '114.
There are a few different ways to challenge patent validity, but if that is something you want to do, your next step is to discuss it with a patent lawyer.