Page 6 in this source: http://www.fanniemae.com/resources/file/ir/pdf/stock-info/series_s_12062007.pdf
In particular, our outstanding subordinated debt securities provide that during any period where interest payments on those debt securities are deferred, dividend payments on our equity securities, includi ng the Preferred Stock, may not be paid.
It is provide that here.
In the dictionary it is provided that or providing that.
How to understand it?
It means that the securities (as contracts or legal agreements) say, hold, or imply (that) . . . (when something happens, something else cannot happen).
The definition is as given here:
2 : to make a proviso or stipulation
the Constitution … provides for an elected two-chamber legislature ...
An additional definition with some examples is given here:
3 [INTRANSITIVE/TRANSITIVE] LEGAL to contain statements or plans that set conditions for dealing with a particular issue
provide for: The treaty provides for the immediate withdrawal of troops from the area.
provide that: Their contracts provide that they will be paid on the last day of the month.
ADDED: @StoneyB's supplementary comment is postpended here for convenience:
Provided that X and providing that X are participle clauses (some would actually categorize them as preposition phrases!) acting as clausal adjuncts: they are in effect conditions (="If and only if X is true") modifying the sense of the main clause. In the sentence you quote provide is the verb which heads the main clause ("our securities provide X").
