I think you don't have to bother yourself with this update, if you rethink your database structure. One great advantage of relational databases is, that you don't need to store the same data several times in several tables, but have one single table for one kind of data (like the person's table in your case) and then reference it (by relationships or foreign keys for example).
So what does this mean for your example? I suggest, to create a institution's table where you insert two attributes like contactperson1 and contactperson2: but dont't insert all the contact details (like email and name), just the primary key of the person and make it a foreign key.
So you got a table 'Person', that should look something like this:
ID INSTITUTION_ID NAME EMAIL
1 100 abc [email protected]
2 101 efg [email protected]
3 101 ijk [email protected]
4 101 rtw [email protected]
...
And a table "Institution" like:
ID CONTACTPERSON1 CONTACTPERSON2
100 1 NULL
101 2 3
...
If you now want to change the email adress, just update the person's table. You don't need to update the firm's table.
And how do you get your desired "table" with the two contact persons' details? Just make a query:
SELECT i.id, p1.name, p1.email, p2.name, p2.email
FROM institution i LEFT OUTER JOIN person p1 ON (i.contactperson1 = p1.id)
LEFT OUTER JOIN person p2 ON (i.contactperson2 = p2.id)
If you need this query often and access it like a "table" just store it as a view.