First, they weren't made with very low quality steel. They were made with bloomery steel, the same as used for most Medieval European swords. The steel comes out of the bloomery as a bloom (in Japanese, a kera), as spongy mass of iron, steel, and slag. This has to be further processed by hammering and folding to get rid of excess slag and to homogenise the steel. This was the usual process over much of the Medieval and Early Modern world.

Second, since the slag content in Ancient and Medieval steelmaking could be and was reduced to acceptable levels by repeated folding of the steel, "low quality" meant either low carbon content or the presence of impurities such as sulphur and phosphorus that could result in brittleness and/or make forging difficult (Japanese swordmaking used ores without such impurities, and carbon contents of 1-1.4% were routinely produced in their smelters). Low carbon content was not at all unusual in Ancient and early Medieval swords, but this typically resulted in soft but tough blades - the swords might not stay sharp for very long, and might stay bent rather than spring back to their original shape when bent, but would be very unlikely to snap like a twig.

That said, swords could be damaged when blocking/parrying or being blocked/parried. This could include damage to the edge, or the blade breaking. Hard edges reduce the likelihood of damage to the edge (if hard edge meets soft edge, the soft edge usually suffers more (but when hard edge meets equally hard edge, hard edges get damaged)). Making the sword resistant to breaking is a compromise between the strength of the sword, the hardness of the edge (harder steels are more likely to crack), and the weight of the sword (generally, thicker = stronger, but this adds weight). Swords, including the katana, were made strong enough to usually survive hitting other blades. But they were also made to be relatively light, and there are many accounts, in fact and contemporary fiction, of swords breaking in use (Western, Japanese, and others).

Finishing a fight in one sword blow, with no contact with the opponent's sword, was an ideal:

You can win with certainty with the spirit of "one cut".

One could try to achieve this by dominating the rhythm of the fight, and not giving the opponent a chance to attack:

In contests of stategy it is bad to be led about by the enemy. You must always be able to lead the enemy about. Obviously the enemy will also be thinking of doing this, but he cannot forestall you if you do not allow him to come out. In strategy, you must stop the enemy as he attempts to cut; you must push down his thrust, and throw off his hold when he tries to grapple. This is the meaning of "to hold down a pillow". When you have grasped this principle, whatever the enemy tries to bring about in the fight you will see in advance and suppress it.

or by good judgment of time and opportunity:

"In One Timing" means, when you have closed with the enemy, to hit him as quickly and directly as possible, without moving your body or settling your spirit, while you see that he is still undecided. The timing of hitting before the enemy decides to withdraw, break or hit, is this "In One Timing".

The timing needed can be created by a feint:

When you attack and the enemy quickly retreats, as you see him tense you must feint a cut. Then, as he relaxes, follow up and hit him. This is the "Abdomen Timing of Two".

However, this ideal was not always attainable, and it was often necessary to defend oneself against the opponent's attack. This could be done by avoiding the blade, by deflecting the blade (parrying), or by stopping the blade with a hard block. All of these were used. The first doesn't damage either blade, the second is unlikely to seriously damage either blade, and the third is likely to at least damage the edges. Typically, avoidance was considered best, and then parrying, and hard-blocking the worst. However, this doesn't appear to have been due to the possibility of damage to swords. This is also the order of preference in boxing, and Dempsey () explained it well:

They can be prevented from landing on their targets by three methods: (1) COMPLETE EVASION of the blow by slipping, bobbing, pulling away or side-stepping; (2) DEFLECTION of the blow by parrying (brushing away) with the hand, or by knifing with the forearm, or by shrugging off with the shoulder; (3) BLOCKING the blow solidly with the hand, forearm, elbow or shoulder.

Evasion is the preferred method. When you force an opponent to miss completely with a blow, he usually lurches off balance and leaves an opening for your counterpunch. Moreover, since the blow has not touched you, it has not off-balanced you for counterpunching.

Deflection is next best; for the parry, glance or shrug usually off-balances your opponent without interfering with your own equilibrium.

Blocking is the least desired; for a solid block not only affects your balance but it also may bruise the spot that makes blocking contact with your opponent's fist.

Basically, a swordsman can counter-cut while an opponent is attacking, taking advantage of the opponent's commitment to the attack and resulting exposure. It is also quicker and easier to counter-attack following a parry than a hard block, and sometimes possible to attack in the same action as parrying (i.e., the technique both parries the attack and hits the opponent).

Parrying and blocking were used by Japanese swordsmen. Instructions for such defensive methods are given:

There are three methods to parry a cut:

First, by dashing the enemy's long sword to your right, as if thrusting at his eyes, when he makes an attack.

Or, to parry by thrusting the enemy's long sword towards his right eye with the feeling of snipping his neck.

Or, when you have a short "long sword", without worrying about parrying the enemy's long sword, to close with him quickly, thrusting at his face with your left hand.

The importance of counter-attack is emphasised:

By "smacking parry" is meant that when you clash swords with the enemy, you meet his attacking cut on your long sword with a tee-dum, tee-dum rhythm, smacking his sword and cutting him. The spirit of the smacking parry is not parrying, or smacking strongly, but smacking the enemy's long sword in accordance with his attacking cut, primarily intent on quickly cutting him.

References:

The quote by Dempsey is from: Jack Dempsey, Championship Fighting, 1950.

The other quotes are from Miyamoto Musashi, Book of Five Rings (Victor Harris translation).

Please see this excellent post on Japanese swords by /u/wotan_weevil